message
stringlengths 2
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values | message_id
int64 0
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int64 575
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float64 16
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int64 1.15k
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|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
|
instruction
| 0
| 575
| 16
| 1,150
|
"Correct Solution:
```
def prepare(n, MOD):
f = 1
factorials = [1] * (n + 1)
for m in range(1, n + 1):
f = f * m % MOD
factorials[m] = f
inv = pow(f, MOD - 2, MOD)
invs = [1] * (n + 1)
invs[n] = inv
for m in range(n, 1, -1):
inv = inv * m % MOD
invs[m - 1] = inv
return factorials, invs
def get_nhr(n, facts, invs, MOD):
def nhr(r):
return facts[n + r - 1] * invs[r] * invs[n - 1] % MOD
return nhr
def solve(n, m):
MOD = 998244353
facts, invs = prepare(n + 3 * m, MOD)
fn = facts[n]
nhr = get_nhr(n, facts, invs, MOD)
nm2 = min(n, m - 1)
ans = 0
for odd in range(m % 2, min(m, n) + 1, 2):
tmp = nhr((3 * m - odd) // 2)
if odd > 0:
tmp -= odd * nhr((m - odd) // 2)
if odd < nm2:
tmp -= (n - odd) * nhr((m - odd - 2) // 2)
ans = (ans + fn * invs[odd] * invs[n - odd] % MOD * tmp) % MOD
return ans
n, m = list(map(int, input().split()))
print(solve(n, m))
```
|
output
| 1
| 575
| 16
| 1,151
|
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
|
instruction
| 0
| 576
| 16
| 1,152
|
"Correct Solution:
```
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
mod=998244353
inv=[0]*(3*M//2+N+2)
inv[1]=1
for i in range(2,3*M//2+N+2):
inv[i]=-(mod//i)*inv[mod%i]%mod
#階乗テーブル
g1=[1,1]
g2=[1,1]
for i in range(2,3*M//2+N+2):
num_1=g1[-1]*i%mod
g1.append(num_1)
g2.append(g2[-1]*inv[i]%mod)
def cmb(n,r):
return g1[n]*g2[r]*g2[n-r]%mod
#奇数の和で場合分け
#iは奇数の数
ans=0
for i in range(min(N+1,M+1)):
if M%2!=i%2:
continue
m=(3*M-i)//2
num=(cmb(m+N-1,N-1)-i*cmb(m-M+N-1,N-1))%mod
if m>=M+1:
num=(num-(N-i)*cmb(m-M+N-2,N-1))%mod
ans=(ans+cmb(N,i)*num)%mod
print(ans)
```
|
output
| 1
| 576
| 16
| 1,153
|
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
|
instruction
| 0
| 577
| 16
| 1,154
|
"Correct Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
from pprint import pprint
from copy import deepcopy
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce
from pprint import pprint
sys.setrecursionlimit(2147483647)
INF = 10 ** 15
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 998244353
n, m = LI()
a = n + 3 * m
fac = [1] * (a + 1)
inv = [1] * (a + 1)
for j in range(1, a + 1):
fac[j] = fac[j-1] * j % mod
inv[a] = pow(fac[a], mod-2, mod)
for j in range(a-1, -1, -1):
inv[j] = inv[j+1] * (j+1) % mod
def comb(x, y):
if y > x or x < 0 or y < 0:
return 0
return fac[x] * inv[x - y] * inv[y] % mod
ans = 0
for i in range(min(m + 1, n + 1)):
if (m - i) % 2:
continue
ans += comb(n, i) * comb((m * 3 - i) // 2 + n - 1, n - 1)
ans %= mod
print((ans - n * comb(m - 1 + n - 1, n - 1)) % mod)
```
|
output
| 1
| 577
| 16
| 1,155
|
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
|
instruction
| 0
| 578
| 16
| 1,156
|
"Correct Solution:
```
n,m = map(int,input().split())
mod = 998244353
#################################
## nCkのmodを求める関数
# テーブルを作る(前処理)
max = n+2*m + 100
fac, finv, inv = [0]*max, [0]*max, [0]*max
def comInit(max):
fac[0] = fac[1] = 1
finv[0] = finv[1] = 1
inv[1] = 1
for i in range(2,max):
fac[i] = fac[i-1]* i% mod
inv[i] = mod - inv[mod%i] * (mod // i) % mod
finv[i] = finv[i-1] * inv[i] % mod
comInit(max)
# 二項係数の計算
def com(n,k):
if(n < k):
return 0
if( (n<0) | (k < 0)):
return 0
return fac[n] * (finv[k] * finv[n-k] % mod) % mod
a = 0
for x in range(min(m,n)+1):
if(3*m-x)%2==1:
continue
y = (3*m-x)//2
a += com(n,x)*fac[y+n-1]*finv[y]*finv[n-1]
a %= mod
b = fac[n-1+m-1] * finv[n-1] * finv[m-1] * n
b %= mod
ans = a-b
ans %= mod
print(ans)
```
|
output
| 1
| 578
| 16
| 1,157
|
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
|
instruction
| 0
| 579
| 16
| 1,158
|
"Correct Solution:
```
class comb():
F = [1, 1]
Fi = [1, 1]
I = [0, 1]
def __init__(self, num, mod):
self.MOD = mod
for i in range(2, num + 1):
self.F.append((self.F[-1] * i) % mod)
self.I.append(mod - self.I[mod % i] * (mod // i) % mod)
self.Fi.append(self.Fi[-1] * self.I[i] % mod)
def com(self, n, k):
if n < k: return 0
if n < 0 or k < 0: return 0
return self.F[n] * (self.Fi[k] * self.Fi[n - k] % self.MOD) % self.MOD
N, M = list(map(int, input().split()))
MOD = 998244353
com = comb(M * 3 + N, MOD)
t = com.com(M * 3 + N - 1, N - 1)
t -= com.com(M - 1 + N - 1, N -1) * N
while t < 0:
t += MOD
if N > M:
for k in range(M + 2, N + 1, 2):
i = (M * 3 - k) // 2
t -= com.com(N, k) * com.com(N - 1 + i, i) % MOD
while t < 0:
t += MOD
print(t)
```
|
output
| 1
| 579
| 16
| 1,159
|
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
|
instruction
| 0
| 580
| 16
| 1,160
|
"Correct Solution:
```
n,m=map(int,input().split())
w,u=3*m,n-1
o,f,i=998244353,[1],1
while i<w+n:f+=[f[-1]*i%o];i+=1
c=lambda n,k=u:f[n]*pow(f[n-k],o-2,o)*pow(f[k],o-2,o)
a=c(w+u)-n*c(n+m-2)
while~-n>m<w:m+=2;a-=c(n,m)*c(2*u+w-m>>1)
print(a%o)
```
|
output
| 1
| 580
| 16
| 1,161
|
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
|
instruction
| 0
| 581
| 16
| 1,162
|
"Correct Solution:
```
n,m=map(int,input().split())
o,f,i=998244353,[1],1
while i<3*m+n:f+=[f[-1]*i%o];i+=1
c=lambda x,y=n-1:f[x]*pow(f[x-y]*f[y]%o,o-2,o)
a=c(-1)-n*c(n+m-2)
while~-n>m<i-n:m+=2;a-=c(n,m)*c(n-1+i-m>>1)
print(a%o)
```
|
output
| 1
| 581
| 16
| 1,163
|
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
|
instruction
| 0
| 582
| 16
| 1,164
|
"Correct Solution:
```
from functools import lru_cache
def prepare(n, MOD):
f = 1
factorials = [1]
for m in range(1, n + 1):
f *= m
f %= MOD
factorials.append(f)
inv = pow(f, MOD - 2, MOD)
invs = [1] * (n + 1)
invs[n] = inv
for m in range(n, 1, -1):
inv *= m
inv %= MOD
invs[m - 1] = inv
return factorials, invs
def get_nhr(n, facts, invs):
@lru_cache(maxsize=None)
def nhr(r):
return facts[n + r - 1] * invs[r] * invs[n - 1] % MOD
return nhr
MOD = 998244353
n, m = list(map(int, input().split()))
facts, invs = prepare(n + 3 * m, MOD)
nhr = get_nhr(n, facts, invs)
ans = 0
for odd in range(m % 2, min(m, n) + 1, 2):
tmp = nhr((3 * m - odd) // 2)
if odd > 0:
tmp -= odd * nhr((m - odd) // 2)
if odd < n and odd <= m - 2:
tmp -= (n - odd) * nhr((m - odd - 2) // 2)
ans = (ans + facts[n] * invs[odd] * invs[n - odd] % MOD * tmp) % MOD
print(ans)
```
|
output
| 1
| 582
| 16
| 1,165
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
Submitted Solution:
```
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
#A
def A():
n = I()
if n <= 1000000000:
print(0,0,1,0,0,n)
else:
b = math.ceil(n**0.5)
if b**2 == n:
print(0,0,b,0,0,n//b)
return
x = b
m = b*x-n
if m < 0:
b += 1
x += 1
m = b*x-n
n = m
for a in range(int(n**0.5)+1)[::-1]:
if n%a == 0:
print(0,0,x,n//a,a,b)
return
return
#B
def B():
n,k = LI()
a = LI()
s = []
f = [1]*1000000
for i in range(k):
for j in range(n):
aj = a[j]
if f[aj]:
s.append(aj)
f[aj] = 0
else:
while 1:
x = s.pop(-1)
f[x] = 1
if x == aj:
break
print(i+1,s)
return
#C
mod = 998244353
def C():
def comb(a,b):
if a < b:
return 1
return fact[a]*inv[b]*inv[a-b]%mod
n,m = LI()
MA = 3*m+max(n,2*m)-1
fact = [1]*(MA+1)
for i in range(MA):
fact[i+1] = fact[i]*(i+1)%mod
inv = [1]*(MA+1)
inv[MA] = pow(fact[MA],mod-2,mod)
for i in range(MA)[::-1]:
inv[i] = inv[i+1]*(i+1)%mod
ans = 0
for k in range(min(m,n)+1):
if (3*m-k)%2 == 0:
ans += comb(n,k)*comb((3*m-k)//2+n-1,n-1)
ans %= mod
ans -= n*comb(3*m-(2*m+1)+n-1,n-1)
ans %= mod
print(ans)
return
#D
def D():
return
#E
def E():
n = I()
return
#F
def F():
n = I()
return
#Solve
if __name__ == "__main__":
C()
```
|
instruction
| 0
| 583
| 16
| 1,166
|
Yes
|
output
| 1
| 583
| 16
| 1,167
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
Submitted Solution:
```
N, M = map(int, input().split())
MOD = 998244353
if N < M :
one = N - (N - M) % 2
two = (3 * M - one) // 2
else :
one, two = M, M
L = M + M // 2 + N - 1
fac = [0] * (L + 1)
inv = [0] * (L + 1)
fac[0], inv[0] = 1, 1
for i in range(1, L + 1) :
fac[i] = fac[i-1] * i % MOD
inv[i] = pow(fac[i], MOD-2, MOD)
def comb(n, r) :
if n <= 0 or r < 0 :
return 0
return fac[n]*inv[n-r]*inv[r]%MOD
ret = 0
while one >= 0 :
ret += comb(N, one) * comb(two+N-1, N-1) % MOD
ret %= MOD
one -= 2
two += 1
ret -= comb(3*M+N-1-(2*M+1), N-1) * N
print(ret % MOD)
```
|
instruction
| 0
| 584
| 16
| 1,168
|
Yes
|
output
| 1
| 584
| 16
| 1,169
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
Submitted Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
from bisect import bisect_left, bisect_right
import random
from itertools import permutations, accumulate, combinations
import sys
import string
INF = float('inf')
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 998244353
n, m = LI()
total = m * 3
fac = [1] * (total+n+1)
inv = [1] * (total+n+1)
for i in range(total+n):
fac[i+1] = fac[i]*(i+1)%mod
inv[total+n]=pow(fac[-1], mod-2, mod)
for j in range(total+n-1, -1, -1):
inv[j]=inv[j+1]*(j+1)%mod
def comb(n, r):
if r > n:
return 0
return fac[n] * inv[n - r] * inv[r] % mod
ans = comb(total+n-1, n-1)
for i in range(m + 2, min(n + 1, total + 1)):
if (total - i) % 2 == 0:
ans -= comb(n, i) * comb(n + (total - i) // 2 - 1, n - 1) % mod
ans %= mod
ret = 0
for i in range(m):
ret = (ret + comb(i + n - 2, n - 2)) % mod
ans -= (ret * n) % mod
print(ans % mod)
```
|
instruction
| 0
| 585
| 16
| 1,170
|
Yes
|
output
| 1
| 585
| 16
| 1,171
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
Submitted Solution:
```
n,m=map(int,input().split())
w,u=3*m,n-1
o,f,i=998244353,[1],1
while i<w+n:f+=[f[-1]*i%o];i+=1
c=lambda n,k:f[n]*pow(f[n-k],o-2,o)*pow(f[k],o-2,o)
a=c(w+u,u)-n*c(n+m-2,u)
while n>-~m<w:m+=2;a-=c(n,m)*c(2*u+w-m>>1,u)
print(a%o)
```
|
instruction
| 0
| 586
| 16
| 1,172
|
Yes
|
output
| 1
| 586
| 16
| 1,173
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
Submitted Solution:
```
import sys
input = sys.stdin.readline
U = 4*10**6
MOD = 998244353
fact = [1]*(U+1)
fact_inv = [1]*(U+1)
for i in range(1,U+1):
fact[i] = (fact[i-1]*i)%MOD
fact_inv[U] = pow(fact[U], MOD-2, MOD)
for i in range(U,0,-1):
fact_inv[i-1] = (fact_inv[i]*i)%MOD
def perm(n, k):
if k < 0 or k > n:
return 0
z = fact[n]
z *= fact_inv[n-k]
z %= MOD
return z
def comb(n, k):
if k < 0 or k > n:
return 0
z = fact[n]
z *= fact_inv[k]
z %= MOD
z *= fact_inv[n-k]
z %= MOD
return z
n, m = map(int, input().split())
ans = 0
for k in range(m%2, min(n, m)+1, 2):
ans += comb((3*m-k)//2+n-1, n-1) * comb(n, k)
ans %= MOD
cnt = 0
for k in range(m):
cnt += comb(k+n-2, n-2)
cnt %= MOD
cnt *= n
cnt %= MOD
ans -= cnt
ans %= MOD
print(ans)
```
|
instruction
| 0
| 587
| 16
| 1,174
|
No
|
output
| 1
| 587
| 16
| 1,175
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
Submitted Solution:
```
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
mod=998244353
#階乗テーブル
g1=[1,1]
for i in range(2,3*M//2+N+2):
g1.append(g1[-1]*i%mod)
def cmb(n,r):
return g1[n]*pow(g1[r],mod-2,mod)*pow(g1[n-r],mod-2,mod)%mod
#奇数の和で場合分け
#iは奇数の数
ans=0
for i in range(min(N+1,M+1)):
if M%2!=i%2:
continue
m=(3*M-i)//2
num=(cmb(m+N-1,N-1)-i*cmb(m-M+N-1,N-1))%mod
if m>=M+1:
num=(num-(N-i)*cmb(m-M+N-2,N-1))%mod
ans=(ans+cmb(N,i)*num)%mod
print(ans)
```
|
instruction
| 0
| 588
| 16
| 1,176
|
No
|
output
| 1
| 588
| 16
| 1,177
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
Submitted Solution:
```
import sys
input = sys.stdin.readline
N,M = map(int,input().split())
mod = 998244353
FACT=[1]
for i in range(1,25*10**5+1):
FACT.append(FACT[-1]*i%mod)
FACT_INV=[pow(FACT[-1],mod-2,mod)]
for i in range(25*10**5,0,-1):
FACT_INV.append(FACT_INV[-1]*i%mod)
FACT_INV.reverse()
def Combi(a,b):
if 0<=b<=a:
return FACT[a]*FACT_INV[b]*FACT_INV[a-b]%mod
else:
return 0
ANS=Combi(M*3+N-1,N-1)
for i in range(M*2+1,M*3+1):
k=M*3-i
ANS=(ANS-N*Combi(k+(N-1)-1,N-2))%mod
for i in range(M+1,N+1):
if (M*3-i)%2==1:
continue
k=(M*3-i)//2
ANS=(ANS-Combi(N,i)*Combi(k+N-1,N-1))%mod
print(ANS)
```
|
instruction
| 0
| 589
| 16
| 1,178
|
No
|
output
| 1
| 589
| 16
| 1,179
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).
Snuke will perform the following operation exactly M times:
* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.
Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.
Constraints
* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different sequences that can result after M operations, modulo 998244353.
Examples
Input
2 2
Output
3
Input
3 2
Output
19
Input
10 10
Output
211428932
Input
100000 50000
Output
3463133
Submitted Solution:
```
import sys
input = sys.stdin.readline
import numpy as np
N,M = map(int,input().split())
MOD = 998244353
def cumprod_mod(arr):
L = len(arr)
Lsq = int(L**.5+1)
arr = np.resize(arr,Lsq**2).reshape(Lsq,Lsq)
for n in range(1,Lsq):
arr[:,n] *= arr[:,n-1]; arr[:,n] %= MOD
for n in range(1,Lsq):
arr[n] *= arr[n-1,-1]; arr[n] %= MOD
arr = arr.ravel()[:L]
return arr
U = 2*10**6 + 100
x = np.arange(U,dtype=np.int64)
x[0] = 1
fact = cumprod_mod(x)
x = np.arange(U,0,-1,dtype=np.int64)
x[0] = pow(int(fact[-1]),MOD-2,MOD)
fact_inv = cumprod_mod(x)[::-1]
def comb(n,k):
return fact[n] * fact_inv[k] % MOD * fact_inv[n-k] % MOD
x = comb(3*M+N-1,N-1) # 何でもいいから作る
y = N * comb(M+N-2,N-1) # どれかが 2M+1 以上
# 奇数がM+1個以上あるものを除く
odd_cnt = np.arange(M+2,3*M+1,2)
S = (3*M - odd_cnt)//2
bl = (odd_cnt <= N)&(S>=0)
odd_cnt = odd_cnt[bl]
S = S[bl]
arr = fact[N] * fact_inv[odd_cnt] % MOD * fact_inv[N-odd_cnt] % MOD
# SをN個で作る -> S+N-1 C N-1
arr *= fact[S+N-1] * fact_inv[N-1] % MOD * fact_inv[S] % MOD
arr %= MOD
z = arr.sum() % MOD
answer = x-y-z
answer %= MOD
print(answer)
```
|
instruction
| 0
| 590
| 16
| 1,180
|
No
|
output
| 1
| 590
| 16
| 1,181
|
Provide a correct Python 3 solution for this coding contest problem.
Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).
He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.
Constraints
* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.
Input
The input is given from Standard Input in the following format:
x_1 y_1
x_2 y_2
x_3 y_3
Output
Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.
Examples
Input
0 0
1 1
2 0
Output
0.292893218813
Input
3 1
1 5
4 9
Output
0.889055514217
|
instruction
| 0
| 655
| 16
| 1,310
|
"Correct Solution:
```
from math import acos, tan, hypot
def getRad1(s12, s13, s23):
return acos((s12*s12 + s13*s13 - s23*s23) / (2*s12*s13))
def getMaxR(s12, rad1, rad2):
tan1 = tan(rad1 / 2)
tan2 = tan(rad2 / 2)
h = s12 * (tan1*tan2) / (tan1+tan2)
return h * (tan1+tan2) / (2*tan1*tan2 + tan1 + tan2)
x1, y1 = map(int, input().split())
x2, y2 = map(int, input().split())
x3, y3 = map(int, input().split())
s12 = hypot(x1-x2, y1-y2)
s23 = hypot(x2-x3, y2-y3)
s31 = hypot(x3-x1, y3-y1)
rad1 = getRad1(s12, s31, s23)
rad2 = getRad1(s23, s12, s31)
rad3 = getRad1(s31, s23, s12)
maxRs = [
getMaxR(s12, rad1, rad2),
getMaxR(s23, rad2, rad3),
getMaxR(s31, rad3, rad1)
]
print(max(maxRs))
```
|
output
| 1
| 655
| 16
| 1,311
|
Provide a correct Python 3 solution for this coding contest problem.
Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).
He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.
Constraints
* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.
Input
The input is given from Standard Input in the following format:
x_1 y_1
x_2 y_2
x_3 y_3
Output
Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.
Examples
Input
0 0
1 1
2 0
Output
0.292893218813
Input
3 1
1 5
4 9
Output
0.889055514217
|
instruction
| 0
| 656
| 16
| 1,312
|
"Correct Solution:
```
xy = [list(map(int, input().split())) for _ in range(3)]
d = [((xy[i][0] - xy[i + 1][0]) ** 2 + (xy[i][1] - xy[i + 1][1]) ** 2) ** .5
for i in range(-1, 2)]
s = abs((xy[1][0] - xy[0][0]) * (xy[2][1] - xy[0][1])
-(xy[2][0] - xy[0][0]) * (xy[1][1] - xy[0][1])) / 2
k = max(d)
r = 2 * s / sum(d)
x = k * r / (k + 2 * r)
print('{:.10f}'.format(x))
```
|
output
| 1
| 656
| 16
| 1,313
|
Provide a correct Python 3 solution for this coding contest problem.
Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).
He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.
Constraints
* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.
Input
The input is given from Standard Input in the following format:
x_1 y_1
x_2 y_2
x_3 y_3
Output
Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.
Examples
Input
0 0
1 1
2 0
Output
0.292893218813
Input
3 1
1 5
4 9
Output
0.889055514217
|
instruction
| 0
| 657
| 16
| 1,314
|
"Correct Solution:
```
import sys
stdin = sys.stdin
sys.setrecursionlimit(10**5)
def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x)-1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())
from math import sqrt
points = [tuple(li()) for _ in range(3)]
# 3つの辺を求める
sides = []
angles = []
for i in range(3):
p1,p2 = points[i], points[(i+1)%3]
sides.append(sqrt((p2[0]-p1[0])**2 + (p2[1]-p1[1])**2))
# 内接円の半径
s = (sum(sides)) / 2
a,b,c = sides
area = sqrt(s* (s-a) * (s-b) * (s-c))
r = 2*area / sum(sides)
print(max(sides)*r / (2*r + max(sides)))
```
|
output
| 1
| 657
| 16
| 1,315
|
Provide a correct Python 3 solution for this coding contest problem.
Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).
He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.
Constraints
* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.
Input
The input is given from Standard Input in the following format:
x_1 y_1
x_2 y_2
x_3 y_3
Output
Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.
Examples
Input
0 0
1 1
2 0
Output
0.292893218813
Input
3 1
1 5
4 9
Output
0.889055514217
|
instruction
| 0
| 658
| 16
| 1,316
|
"Correct Solution:
```
x1, y1 = map(int, input().split())
x2, y2 = map(int, input().split())
x3, y3 = map(int, input().split())
e12 = ((x2-x1)**2 + (y2-y1)**2)**0.5
e23 = ((x3-x2)**2 + (y3-y2)**2)**0.5
e31 = ((x1-x3)**2 + (y1-y3)**2)**0.5
s = (e12 + e23 + e31)/2
S = (s * (s-e12) * (s-e23) * (s-e31)) ** 0.5
r=2*S/(e12+e23+e31)
A=max(e12,e23,e31)
print(A*r/(2*r+A))
```
|
output
| 1
| 658
| 16
| 1,317
|
Provide a correct Python 3 solution for this coding contest problem.
Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).
He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.
Constraints
* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.
Input
The input is given from Standard Input in the following format:
x_1 y_1
x_2 y_2
x_3 y_3
Output
Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.
Examples
Input
0 0
1 1
2 0
Output
0.292893218813
Input
3 1
1 5
4 9
Output
0.889055514217
|
instruction
| 0
| 659
| 16
| 1,318
|
"Correct Solution:
```
import sys
input = sys.stdin.readline
#import heapq
#from fractions import gcd
#from collections import defaultdict
#sys.setrecursionlimit(10**9)
#map(int,input().split())
def main():
li=[list(map(int,input().split())) for i in range(3)]
li.append(li[0])
d=[0]*3
for i in range(3):
d[i]=((li[i][0]-li[i+1][0])**2+(li[i][1]-li[i+1][1])**2)**0.5
dmax=max(d)
dsum=sum(d)
s=dsum/2
S=(s*(s-d[0])*(s-d[1])*(s-d[2]))**0.5
r=2*S/dsum
print((r*dmax)/(2*r+dmax))
if __name__ == '__main__':
main()
```
|
output
| 1
| 659
| 16
| 1,319
|
Provide a correct Python 3 solution for this coding contest problem.
Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).
He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.
Constraints
* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.
Input
The input is given from Standard Input in the following format:
x_1 y_1
x_2 y_2
x_3 y_3
Output
Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.
Examples
Input
0 0
1 1
2 0
Output
0.292893218813
Input
3 1
1 5
4 9
Output
0.889055514217
|
instruction
| 0
| 660
| 16
| 1,320
|
"Correct Solution:
```
p1 = list(map(int, input().split()))
p2 = list(map(int, input().split()))
p3 = list(map(int, input().split()))
len1 = ((p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2) ** 0.5
len2 = ((p2[0] - p3[0]) ** 2 + (p2[1] - p3[1]) ** 2) ** 0.5
len3 = ((p3[0] - p1[0]) ** 2 + (p3[1] - p1[1]) ** 2) ** 0.5
l = (len1 + len2 + len3) / 2
s = (l * (l - len1) * (l - len2) * (l - len3)) ** 0.5
r = 2 * s /(len1 + len2 + len3)
def solve(mid):
return (1 - mid / r) * max(len1, len2, len3) >= 2 * mid
ok = 0
ng = 10 ** 9
cnt = 0
while True:
mid = (ok + ng) / 2
if solve(mid):
ok = mid
else:
ng = mid
cnt += 1
if cnt > 60:
break
print(ok)
```
|
output
| 1
| 660
| 16
| 1,321
|
Provide a correct Python 3 solution for this coding contest problem.
Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).
He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.
Constraints
* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.
Input
The input is given from Standard Input in the following format:
x_1 y_1
x_2 y_2
x_3 y_3
Output
Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.
Examples
Input
0 0
1 1
2 0
Output
0.292893218813
Input
3 1
1 5
4 9
Output
0.889055514217
|
instruction
| 0
| 661
| 16
| 1,322
|
"Correct Solution:
```
a,b,c,d,e,f=map(int,open(0).read().split())
a,b,c=sorted((s*s+t*t)**.5for s,t in((a-c,b-d),(c-e,d-f),(e-a,f-b)))
d=a+b+c
s=d/2
s=(s*(s-a)*(s-b)*(s-c))**.5
print(c/(2+c/2/s*d))
```
|
output
| 1
| 661
| 16
| 1,323
|
Provide a correct Python 3 solution for this coding contest problem.
Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).
He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.
Constraints
* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.
Input
The input is given from Standard Input in the following format:
x_1 y_1
x_2 y_2
x_3 y_3
Output
Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.
Examples
Input
0 0
1 1
2 0
Output
0.292893218813
Input
3 1
1 5
4 9
Output
0.889055514217
|
instruction
| 0
| 662
| 16
| 1,324
|
"Correct Solution:
```
def OuterProduct(one, two):
tmp = one.conjugate() * two
return tmp.imag
def Area(dots):
res = 0
for i in range(len(dots)-1):
res += OuterProduct(dots[i], dots[i+1])
res += OuterProduct(dots[-1], dots[0])
return res/2
d = [list(map(int, input().split())) for _ in range(3)]
x = complex(d[0][0], d[0][1])
y = complex(d[1][0], d[1][1])
z = complex(d[2][0], d[2][1])
s = abs(Area([x, y, z]))
a, b, c = abs(x-y), abs(y-z), abs(z-x)
print(2*s/(a+b+c+(4*s/max(a, b, c))))
```
|
output
| 1
| 662
| 16
| 1,325
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).
He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.
Constraints
* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.
Input
The input is given from Standard Input in the following format:
x_1 y_1
x_2 y_2
x_3 y_3
Output
Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.
Examples
Input
0 0
1 1
2 0
Output
0.292893218813
Input
3 1
1 5
4 9
Output
0.889055514217
Submitted Solution:
```
from math import hypot
p = [list(map(int, input().split())) for i in range(3)]
x1 = p[1][0] - p[0][0]
y1 = p[1][1] - p[0][1]
x2 = p[2][0] - p[0][0]
y2 = p[2][1] - p[0][1]
s2 = abs(x1*y2-x2*y1)
s = 0
m = 0
for i in range(3):
x = p[i-1][0]-p[i][0]
y = p[i-1][1]-p[i][1]
l = hypot(x, y)
s += l
m = max(m, l)
r = s2/s
x = m*r/(2*r+m)
print(x)
```
|
instruction
| 0
| 665
| 16
| 1,330
|
Yes
|
output
| 1
| 665
| 16
| 1,331
|
Provide a correct Python 3 solution for this coding contest problem.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
|
instruction
| 0
| 1,508
| 16
| 3,016
|
"Correct Solution:
```
import sys
input = sys.stdin.readline
MOD = pow(10, 9) + 7
def main():
n = int(input())
alist = list(map(int, input().split()))
nn = 1
for i in range(2, n+1):
nn = nn * i % MOD
rev = [pow(i, MOD-2, MOD) * nn % MOD for i in range(1, n+1)]
for i in range(1, n):
rev[i] = (rev[i] + rev[i-1]) % MOD
ans = 0
for i in range(n):
ans += alist[i] * (rev[i] + rev[n-i-1] - rev[0]) % MOD
ans %= MOD
print(ans)
if __name__ == '__main__':
main()
```
|
output
| 1
| 1,508
| 16
| 3,017
|
Provide a correct Python 3 solution for this coding contest problem.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
|
instruction
| 0
| 1,509
| 16
| 3,018
|
"Correct Solution:
```
def multiply(x, y):
return (x * y) % mod
def power(x, y):
if y == 0:
return 1
elif y == 1:
return x
elif x == 1:
return 1
elif x == 0:
return 0
else:
# print(mod)
tmp = power(x, y // 2)
return (multiply(tmp, tmp) * [1, x][y % 2]) % mod
N = int(input())
A = list(map(int, input().split()))
mod = 10 ** 9 + 7
plist = [0]
nfact = 1
N
tmp = 0
for i in range(1, N):
tmp = (tmp + power(i + 1, mod - 2)) % mod
nfact = (nfact * (i + 1)) % mod
plist.append(tmp)
ans = 0
# print(plist)
# print(nfact)
for i, a in enumerate(A):
# print(i, N - i - 1, N)
tmp = (1 + plist[i] + plist[N - i - 1]) % mod
ans = (ans + multiply(multiply(a, tmp), nfact)) % mod
print(ans)
```
|
output
| 1
| 1,509
| 16
| 3,019
|
Provide a correct Python 3 solution for this coding contest problem.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
|
instruction
| 0
| 1,510
| 16
| 3,020
|
"Correct Solution:
```
N = int(input())
A = [int(a) for a in input().split()]
P = 10**9+7
def inv(a):
return pow(a, P-2, P)
s = 0
for i in range(N):
s += inv(i+1)
ans = 0
for i in range(N):
ans += s * A[i]
ans %= P
s += inv(i+2) - inv(N-i)
for i in range(1, N+1):
ans = ans * i % P
print(ans)
```
|
output
| 1
| 1,510
| 16
| 3,021
|
Provide a correct Python 3 solution for this coding contest problem.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
|
instruction
| 0
| 1,511
| 16
| 3,022
|
"Correct Solution:
```
inv=lambda x:pow(x, m - 2, m)
N = int(input())
A = [int(x) for x in input().split()]
f = [1, 1]
m = 10**9+7
for i in range(2, N + 1):
f+=[f[-1] * i % m]
s = [0]
for i in range(1, N + 1):
s+=[(s[-1]+f[N]*inv(i))%m]
a = 0
for i in range(N):
a+=(s[i+1]+s[N-i]-f[N])*A[i]
a%=m
print(a)
```
|
output
| 1
| 1,511
| 16
| 3,023
|
Provide a correct Python 3 solution for this coding contest problem.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
|
instruction
| 0
| 1,512
| 16
| 3,024
|
"Correct Solution:
```
mod=10**9+7
N=int(input())
a=[int(i) for i in input().split()]
F=1
for i in range(1,N+1):
F=(F*i)%mod
def power(x,y):
if y==0:
return 1
elif y==1:
return x%mod
elif y%2==0:
return power(x,y//2)**2%mod
else:
return (power(x,y//2)**2)*x%mod
inv=[0]*(N)
for i in range(N):
inv[i]=power(i+1,mod-2)
S_inv=[0]*(N+1)
for i in range(N):
S_inv[i+1]=S_inv[i]+inv[i]
ans=0
for i in range(N):
p=S_inv[i+1]+S_inv[N-i]-1
ans=(ans+a[i]*F*p)%mod
print(ans)
```
|
output
| 1
| 1,512
| 16
| 3,025
|
Provide a correct Python 3 solution for this coding contest problem.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
|
instruction
| 0
| 1,513
| 16
| 3,026
|
"Correct Solution:
```
def prepare(n, MOD):
f = 1
factorials = [1]
for m in range(1, n + 1):
f *= m
f %= MOD
factorials.append(f)
inv = pow(f, MOD - 2, MOD)
invs = [1] * (n + 1)
invs[n] = inv
for m in range(n, 1, -1):
inv *= m
inv %= MOD
invs[m - 1] = inv
return factorials, invs
def solve(n, aaa):
factorials, invs = prepare(n, MOD)
fn = factorials[n]
coefs = [fn * invs[i + 1] * factorials[i] % MOD for i in range(1, n)]
acc = [0]
for c in coefs:
tmp = (acc[-1] + c) % MOD
acc.append(tmp)
ans = 0
for i, a in enumerate(aaa):
ans += (acc[i] + acc[n - i - 1] + fn) * a
ans %= MOD
return ans
MOD = 1000000007
n = int(input())
aaa = list(map(int, input().split()))
print(solve(n, aaa))
```
|
output
| 1
| 1,513
| 16
| 3,027
|
Provide a correct Python 3 solution for this coding contest problem.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
|
instruction
| 0
| 1,514
| 16
| 3,028
|
"Correct Solution:
```
n = int(input())
A = [int(i) for i in input().split()]
p = 10 ** 9 + 7
def fact(n, p=10**9 + 7):
f = 1
for i in range(1, n+1):
f *= i
f %= p
return f
def get_inv(n, p=10**9 + 7):
inv = [0, 1]
for i in range(2, n+1):
inv.append(-(p//i * inv[p%i]) % p)
return inv
f = fact(n)
inv = get_inv(n)
csum = [0]
for i in range(1, n+1):
csum.append((csum[-1] + inv[i]) % p)
ans = 0
for i, a in enumerate(A):
ans += (csum[i+1] + csum[n-i] - csum[1] + p) % p * a
ans %= p
print(ans * f % p)
```
|
output
| 1
| 1,514
| 16
| 3,029
|
Provide a correct Python 3 solution for this coding contest problem.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
|
instruction
| 0
| 1,515
| 16
| 3,030
|
"Correct Solution:
```
# B
N = int(input())
A_list = list(map(int, input().split()))
LARGE = 10**9+7
def pinv(p, k):
return pow(k, p-2, p)
Npow = 1
for i in range(2, N+1):
Npow = Npow*i % LARGE
K = 0
for i in range(N):
K += pinv(LARGE, i+1)
res = (K*A_list[0]) % LARGE
for i in range(1, N):
K -= pinv(LARGE, N+1-i)
K += pinv(LARGE, i+1)
res = (res + K*A_list[i]) % LARGE
print(res*Npow % LARGE)
```
|
output
| 1
| 1,515
| 16
| 3,031
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
Submitted Solution:
```
N = int(input())
*A, = map(int, input().split())
MOD = 10**9 + 7
S = [0]*(N+1)
r = 0
for i in range(1, N+1):
S[i] = r = (r + pow(i, MOD-2, MOD)) % MOD
ans = 0
for i in range(N):
ans += A[i] * (S[i+1] + S[N-i] - 1)
for i in range(1, N+1):
ans = ans * i % MOD
print(ans)
```
|
instruction
| 0
| 1,516
| 16
| 3,032
|
Yes
|
output
| 1
| 1,516
| 16
| 3,033
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
Submitted Solution:
```
N = int(input())
A = list(map(int,input().split()))
mod = 10**9+7
def inv(n):
n %= mod
return pow(n,mod-2,mod)
H = [0]*(N+1)
for n in range(1,N+1):
H[n] = (inv(n)+H[n-1])%mod
N_f = 1
for n in range(1,N+1):
N_f = N_f*n%mod
ans = 0
for n in range(1,N+1):
ans += A[n-1]*(H[N-n+1]+H[n]-1)
ans %= mod
ans *= N_f
ans %= mod
print(ans)
```
|
instruction
| 0
| 1,517
| 16
| 3,034
|
Yes
|
output
| 1
| 1,517
| 16
| 3,035
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
Submitted Solution:
```
def main():
n = int(input())
a = list(map(int, input().split()))
mod, fact, m, npr, now = 10**9+7, [1, 1], [0, 1], [1]*(n+1), 1
for i in range(2, n+1):
fact.append(fact[-1]*i % mod)
for i in range(n, 0, -1):
npr[i-1] = npr[i]*i % mod
for i in range(2, n+1):
m.append(fact[i]+now)
now = (m[-1]+now*i) % mod
m = [i*j % mod for i, j in zip(npr, m)]
ans = (sum([j*(m[n-i]+m[i+1])
for i, j in enumerate(a)])-sum(a)*fact[n]) % mod
print(ans)
main()
```
|
instruction
| 0
| 1,518
| 16
| 3,036
|
Yes
|
output
| 1
| 1,518
| 16
| 3,037
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
Submitted Solution:
```
# -*- coding: utf-8 -*-
import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, sub
sys.setrecursionlimit(10000)
mod = 10**9 + 7
def read_int():
return int(input())
def read_int_n():
return list(map(int, input().split()))
def read_float():
return float(input())
def read_float_n():
return list(map(float, input().split()))
def read_str():
return input().strip()
def read_str_n():
return list(map(str, input().split()))
def error_print(*args):
print(*args, file=sys.stderr)
def mt(f):
import time
def wrap(*args, **kwargs):
s = time.time()
ret = f(*args, **kwargs)
e = time.time()
error_print(e - s, 'sec')
return ret
return wrap
def mul(a, b):
return ((a % mod) * (b % mod)) % mod
def power(x, y):
if y == 0:
return 1
elif y == 1:
return x % mod
elif y % 2 == 0:
return power(x, y//2)**2 % mod
else:
return power(x, y//2)**2 * x % mod
def div(a, b):
return mul(a, power(b, mod-2))
@mt
def slv(N, A):
def perm(n):
p = 1
for i in range(1, n+1):
p *= i
p %= mod
return p
pn = perm(N)
sp = [0]
for i in range(1, N+1):
sp.append((sp[-1] + div(pn, i)) % mod)
ans = mul(sp[-1], A[0])
for i in range(1, N):
ans += mul(sp[i+1] - sp[1], A[i])
ans %= mod
ans += mul(sp[N-i] - sp[0], A[i])
ans %= mod
return ans
def main():
N = read_int()
A = read_int_n()
print(slv(N, A))
if __name__ == '__main__':
main()
```
|
instruction
| 0
| 1,519
| 16
| 3,038
|
Yes
|
output
| 1
| 1,519
| 16
| 3,039
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
Submitted Solution:
```
import sys
fin = sys.stdin.readline
def factorial(n, mod):
if n == 0:
return 1
else:
return n * factorial(n - 1, mod) % mod
MOD = 10**9 + 7
N = int(fin())
A_list = [int(elem) for elem in fin().split()]
fac_N = factorial(N, MOD)
inv_nums = [fac_N * pow(i, MOD - 2, MOD) % MOD for i in range(1, N + 1)]
cuml_inv_nums = [inv_nums[0]]
for inv_num in inv_nums[1:]:
cuml_inv_nums.append((cuml_inv_nums[-1] + inv_num) % MOD)
ans = 0
for i, A in enumerate(A_list):
ans += A * (cuml_inv_nums[i] + cuml_inv_nums[N - 1 - i] - cuml_inv_nums[0]) % MOD
ans %= MOD
print(ans)
```
|
instruction
| 0
| 1,520
| 16
| 3,040
|
No
|
output
| 1
| 1,520
| 16
| 3,041
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
Submitted Solution:
```
import numpy as np
n = int(input())
li = list(map(int, input().split()))
def weight(li,ansli):
if li == []:
return
a = sum(li)
for j in range(len(li)):
a = a*(j+1)
ansli.append(a)
for i in range(len(li)):
weight(li[:i],ansli)
weight(li[i+1:],ansli)
return ansli
print(sum(weight(li,[]))%(10**9+7))
```
|
instruction
| 0
| 1,521
| 16
| 3,042
|
No
|
output
| 1
| 1,521
| 16
| 3,043
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
Submitted Solution:
```
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
"""
AGC028 B
"""
import itertools
n = int(input())
ali = list(map(int, input().split()))
cut = 10**9+7
def modInverse(a, b, divmod=divmod):
r0, r1, s0, s1 = a, b, 1, 0
while r1 != 0:
q, rtmp = divmod(r0, r1)
stmp = s0-q*s1
r0, s0 = r1, s1
r1, s1 = rtmp, stmp
return s0 % cut
def factorial(n):
nn = 1
for i in range(2, n+1):
nn = nn*i
return(nn)
invlist = [modInverse(i, cut) for i in range(1, n+1)]
accuminv = list(itertools.accumulate(invlist, func=lambda x, y: x+y % cut))
ans = 0
nfact = factorial(n)
for i in range(n):
sump = accuminv[i]+accuminv[n-1-i] - 1
ans += ali[i]*sump % cut
ans = ans*nfact % cut
print(ans)
```
|
instruction
| 0
| 1,522
| 16
| 3,044
|
No
|
output
| 1
| 1,522
| 16
| 3,045
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N blocks arranged in a row, numbered 1 to N from left to right. Each block has a weight, and the weight of Block i is A_i. Snuke will perform the following operation on these blocks N times:
* Choose one block that is still not removed, and remove it. The cost of this operation is the sum of the weights of the blocks that are connected to the block being removed (including itself). Here, two blocks x and y ( x \leq y ) are connected when, for all z ( x \leq z \leq y ), Block z is still not removed.
There are N! possible orders in which Snuke removes the blocks. For all of those N! orders, find the total cost of the N operations, and calculate the sum of those N! total costs. As the answer can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For all of the N! orders, find the total cost of the N operations, and print the sum of those N! total costs, modulo 10^9+7.
Examples
Input
2
1 2
Output
9
Input
4
1 1 1 1
Output
212
Input
10
1 2 4 8 16 32 64 128 256 512
Output
880971923
Submitted Solution:
```
N = int(input())
w = [int(i) for i in input().split())]
def f(n):
i = 1
for j in range(0,n):
i = i*(j+1)
return i
def c(l):
n = len(l)
if n == 0
return 0
elif n == 1:
return l[0]
else:
t = f(n)*sum(l)
for i in range(0,n):
a = l[0:i]
b = l[i+1:n]
t = t + (f(n-1)/f(i))*c(a) + (f(n-1)/f(n-i-1))*c(b)
return int(t)
print(c(w))
```
|
instruction
| 0
| 1,523
| 16
| 3,046
|
No
|
output
| 1
| 1,523
| 16
| 3,047
|
Provide a correct Python 3 solution for this coding contest problem.
There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.
Snuke can apply the following operation to this grid any number of times:
* Choose two different rows and swap them. Or, choose two different columns and swap them.
Snuke wants this grid to be symmetric. That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Constraints
* 1 \leq H \leq 12
* 1 \leq W \leq 12
* |S_i| = W
* S_i consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H
Output
If Snuke can make the grid symmetric, print `YES`; if he cannot, print `NO`.
Examples
Input
2 3
arc
rac
Output
YES
Input
3 7
atcoder
regular
contest
Output
NO
Input
12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv
Output
YES
|
instruction
| 0
| 1,524
| 16
| 3,048
|
"Correct Solution:
```
H, W = map(int, input().split())
Ss = [input() for _ in range(H)]
# 行の入れ替えパターンを生成する（中央付近から埋めていく）
def dfs(iR):
# 全て埋まったら、判定に移る
if iR < 0:
return check()
# 未使用の行を検索する
iF = flgs.index(False)
Rs[iR] = iF - offset
flgs[iF] = True
# ペアの相手を決めて、次のペア生成に移る
ans = False
for iF2, flg in enumerate(flgs):
if not flg:
Rs[H - 1 - iR] = iF2 - offset
flgs[iF2] = True
ans = ans or dfs(iR - 1)
flgs[iF2] = False
flgs[iF] = False
return ans
# 与えられた行の入れ替えパターンに対して、列の入れ替えのみで点対称にできるかを判定する
def check():
Ts = [Ss[R] for R in Rs]
Ts = list(map(list, zip(*Ts)))
# (W+1)/2列目を使用可能かどうか
if W % 2: flgCenter = True
else: flgCenter = False
# 各列に対して、処理を行う
Used = [False] * W
for j, T in enumerate(Ts):
if Used[j]: continue
for j2, T2 in enumerate(Ts[j + 1:], j + 1):
# 上下反転したような未使用の列が存在するならば、次の列へ
if not Used[j2] and T[::-1] == T2:
Used[j2] = True
break
else:
# 自身が上下対称、かつ、(W+1)/2列目を使用可能ならば、次の列へ
if T[::-1] == T and flgCenter == True:
flgCenter = False
else:
# この入れ替えパターンでは不可能と判定
return False
return True
if H % 2:
# Hが奇数ならば、先頭にダミーを付加
flgs = [False] * (H + 1)
offset = 1
else:
flgs = [False] * H
offset = 0
Rs = [-1] * H
if dfs((H - 1) // 2):
print('YES')
else:
print('NO')
```
|
output
| 1
| 1,524
| 16
| 3,049
|
Provide a correct Python 3 solution for this coding contest problem.
There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.
Snuke can apply the following operation to this grid any number of times:
* Choose two different rows and swap them. Or, choose two different columns and swap them.
Snuke wants this grid to be symmetric. That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Constraints
* 1 \leq H \leq 12
* 1 \leq W \leq 12
* |S_i| = W
* S_i consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H
Output
If Snuke can make the grid symmetric, print `YES`; if he cannot, print `NO`.
Examples
Input
2 3
arc
rac
Output
YES
Input
3 7
atcoder
regular
contest
Output
NO
Input
12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv
Output
YES
|
instruction
| 0
| 1,525
| 16
| 3,050
|
"Correct Solution:
```
def check(field):
tr = list(map(''.join, zip(*field)))
paired = set()
center = -1
for i, col1 in enumerate(tr):
if i in paired:
continue
for j, col2 in enumerate(tr[i + 1:], start=i + 1):
if j in paired:
continue
if col1 == col2[::-1]:
paired.add(i)
paired.add(j)
break
else:
if center == -1 and col1 == col1[::-1]:
center = i
else:
return False
return True
def arrange_row(field, new_field, i, remain):
if len(remain) == 0:
return check(new_field)
j = remain.pop()
new_field[i] = field[j]
for k in list(remain):
remain.remove(k)
new_field[h - i - 1] = field[k]
result = arrange_row(field, new_field, i + 1, remain)
if result:
return True
remain.add(k)
remain.add(j)
return False
def solve(h, w, field):
new_field = [None] * h
remaining_row = set(range(h))
if h % 2 == 0:
return arrange_row(field, new_field, 0, remaining_row)
for i in list(remaining_row):
remaining_row.remove(i)
new_field[h // 2] = field[i]
result = arrange_row(field, new_field, 0, remaining_row)
if result:
return True
remaining_row.add(i)
return False
h, w = map(int, input().split())
field = [input() for _ in range(h)]
print('YES' if solve(h, w, field) else 'NO')
```
|
output
| 1
| 1,525
| 16
| 3,051
|
Provide a correct Python 3 solution for this coding contest problem.
There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.
Snuke can apply the following operation to this grid any number of times:
* Choose two different rows and swap them. Or, choose two different columns and swap them.
Snuke wants this grid to be symmetric. That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Constraints
* 1 \leq H \leq 12
* 1 \leq W \leq 12
* |S_i| = W
* S_i consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H
Output
If Snuke can make the grid symmetric, print `YES`; if he cannot, print `NO`.
Examples
Input
2 3
arc
rac
Output
YES
Input
3 7
atcoder
regular
contest
Output
NO
Input
12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv
Output
YES
|
instruction
| 0
| 1,526
| 16
| 3,052
|
"Correct Solution:
```
import os
import sys
if os.getenv("LOCAL"):
sys.stdin = open("_in.txt", "r")
sys.setrecursionlimit(10 ** 9)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7
# MOD = 998244353
H, W = list(map(int, sys.stdin.buffer.readline().split()))
S = [sys.stdin.buffer.readline().decode().rstrip() for _ in range(H)]
# ペアのとり方は 10395 通り
# a = math.factorial(12) / (2 ** 6) / math.factorial(6)
# print(a) # 10395
def test(groups):
seen = [False] * 6
order = [-1] * len(groups)
for i, g in enumerate(groups):
if g == -1:
# 真ん中
order[W // 2] = i
continue
if not seen[g]:
order[g] = i
seen[g] = True
else:
order[~g] = i
# print(groups, order)
# return False
rows = []
for s in S:
row = ''
for i in order:
row += s[i]
rows.append(row)
ok = [False] * H
for i in range(H):
if ok[i]:
continue
rev = rows[i][::-1]
for j in range(i + 1, H):
if not ok[j] and rows[j] == rev:
ok[i] = ok[j] = True
break
ng_cnt = ok.count(False)
if ng_cnt == 0:
return True
if ng_cnt == 1:
i = ok.index(False)
return rows[i] == rows[i][::-1]
return False
def solve(groups, depth=0):
if depth == W // 2:
return test(groups)
i = 0
for _ in range(2 if W % 2 == 1 else 1):
while groups[i] != -1:
i += 1
groups[i] = depth
for j in range(i + 1, W):
if groups[j] != -1:
continue
groups[j] = depth
if solve(groups, depth + 1):
return True
groups[j] = -1
groups[i] = -1
i += 1
return False
groups = [-1] * W
ok = solve(groups)
if ok:
print('YES')
else:
print('NO')
```
|
output
| 1
| 1,526
| 16
| 3,053
|
Provide a correct Python 3 solution for this coding contest problem.
There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.
Snuke can apply the following operation to this grid any number of times:
* Choose two different rows and swap them. Or, choose two different columns and swap them.
Snuke wants this grid to be symmetric. That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Constraints
* 1 \leq H \leq 12
* 1 \leq W \leq 12
* |S_i| = W
* S_i consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H
Output
If Snuke can make the grid symmetric, print `YES`; if he cannot, print `NO`.
Examples
Input
2 3
arc
rac
Output
YES
Input
3 7
atcoder
regular
contest
Output
NO
Input
12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv
Output
YES
|
instruction
| 0
| 1,527
| 16
| 3,054
|
"Correct Solution:
```
H,W=map(int,input().split())
G=[list(input()) for i in range(H)]
G_t=[list(x) for x in list(zip(*G))]
def Check(G,H,W):
Paired_y=[False]*H
for y1 in range(H):
if Paired_y[y1]:
continue
for y2 in range(H):
if y1==y2 or Paired_y[y2]:
continue
Paired_x=[False]*W
for x1 in range(W):
if Paired_x[x1]:
continue
for x2 in range(W):
if x1==x2 or Paired_x[x2]:
continue
if G[y1][x1]==G[y2][x2] and G[y1][x2]==G[y2][x1]:
Paired_x[x1]=True
Paired_x[x2]=True
break
if W%2==1:
if Paired_x.count(False)==1:
r=Paired_x.index(False)
if G[y1][r]==G[y2][r]:
Paired_y[y1]=True
Paired_y[y2]=True
break
else:
if Paired_x.count(False)==0:
Paired_y[y1]=True
Paired_y[y2]=True
break
if H%2==1:
if Paired_y.count(False)==1:
return True
else:
return False
else:
if Paired_y.count(False)==0:
return True
else:
return False
if Check(G,H,W) and Check(G_t,W,H):
print("YES")
else:
print("NO")
```
|
output
| 1
| 1,527
| 16
| 3,055
|
Provide a correct Python 3 solution for this coding contest problem.
There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.
Snuke can apply the following operation to this grid any number of times:
* Choose two different rows and swap them. Or, choose two different columns and swap them.
Snuke wants this grid to be symmetric. That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Constraints
* 1 \leq H \leq 12
* 1 \leq W \leq 12
* |S_i| = W
* S_i consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H
Output
If Snuke can make the grid symmetric, print `YES`; if he cannot, print `NO`.
Examples
Input
2 3
arc
rac
Output
YES
Input
3 7
atcoder
regular
contest
Output
NO
Input
12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv
Output
YES
|
instruction
| 0
| 1,528
| 16
| 3,056
|
"Correct Solution:
```
H, W = map(int, input().split())
S = [input() for i in range(H)]
def check(l):
u = [0]*W
mid = W % 2
for i in range(W):
if u[i]:
continue
for j in range(i+1, W):
for p, q in l:
sp = S[p]; sq = S[q]
if sp[i] != sq[j] or sp[j] != sq[i]:
break
else:
u[j] = 1
break
else:
if mid:
for p, q in l:
sp = S[p]; sq = S[q]
if sp[i] != sq[i]:
break
else:
mid = 0
continue
break
else:
return 1
return 0
def make(c, l, u, p):
while c in u:
c += 1
if c == H:
if check(l):
print("YES")
exit(0)
return
if p:
l.append((c, c))
make(c+1, l, u, 0)
l.pop()
for i in range(c+1, H):
if i in u:
continue
u.add(i)
l.append((c, i))
make(c+1, l, u, p)
l.pop()
u.remove(i)
make(0, [], set(), H%2)
print("NO")
```
|
output
| 1
| 1,528
| 16
| 3,057
|
Provide a correct Python 3 solution for this coding contest problem.
There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.
Snuke can apply the following operation to this grid any number of times:
* Choose two different rows and swap them. Or, choose two different columns and swap them.
Snuke wants this grid to be symmetric. That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Constraints
* 1 \leq H \leq 12
* 1 \leq W \leq 12
* |S_i| = W
* S_i consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H
Output
If Snuke can make the grid symmetric, print `YES`; if he cannot, print `NO`.
Examples
Input
2 3
arc
rac
Output
YES
Input
3 7
atcoder
regular
contest
Output
NO
Input
12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv
Output
YES
|
instruction
| 0
| 1,529
| 16
| 3,058
|
"Correct Solution:
```
import sys
import copy
sys.setrecursionlimit(10 ** 6)
def main():
def per(s, a=[]):
if not s:
return [a]
if len(s) % 2:
cs = copy.deepcopy(s)
res = []
for u in cs:
s.remove(u)
res += per(s, [u] + a)
s.add(u)
return res
u = min(s)
s.remove(u)
cs = copy.deepcopy(s)
res = []
for uu in cs:
if uu < u: continue
s.remove(uu)
res += per(s, a + [u, uu])
s.add(uu)
s.add(u)
return res
ord_a = ord("a")
h, w = map(int, input().split())
t0 = [[ord(c) - ord_a for c in input()] for _ in range(h)]
h_set = set(range(h))
pattern = per(h_set)
# print(t0)
# print(pattern)
b = h % 2
for p in pattern:
t1 = [[] for _ in range(h)]
if b:
t1[h // 2] = t0[p[0]]
i = 0
for ii in range(b, h, 2):
t1[i] = t0[p[ii]]
t1[h - 1 - i] = t0[p[ii + 1]]
i += 1
# print(p)
# print(t1)
fin = [False] * w
mid = (w % 2 == 1)
br = False
for j, c0 in enumerate(zip(*t1)):
if fin[j]: continue
fin[j] = True
c0 = c0[::-1]
for jj, c1 in enumerate(zip(*t1)):
if jj <= j: continue
if fin[jj]: continue
if c0 == c1:
fin[jj] = True
break
else:
if mid and c0 == c0[::-1]:
mid = False
else:
br = True
break
if br: continue
print("YES")
exit()
print("NO")
main()
```
|
output
| 1
| 1,529
| 16
| 3,059
|
Provide a correct Python 3 solution for this coding contest problem.
There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.
Snuke can apply the following operation to this grid any number of times:
* Choose two different rows and swap them. Or, choose two different columns and swap them.
Snuke wants this grid to be symmetric. That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Constraints
* 1 \leq H \leq 12
* 1 \leq W \leq 12
* |S_i| = W
* S_i consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H
Output
If Snuke can make the grid symmetric, print `YES`; if he cannot, print `NO`.
Examples
Input
2 3
arc
rac
Output
YES
Input
3 7
atcoder
regular
contest
Output
NO
Input
12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv
Output
YES
|
instruction
| 0
| 1,530
| 16
| 3,060
|
"Correct Solution:
```
# この解法は嘘を含む
from itertools import groupby
H, W = map(int, input().split())
S_ = ["" for _ in range(W)]
T_ = []
for _ in range(H):
s = input()
T_.append(s)
for i, c in enumerate(s):
S_[i] += c
T = [sorted(t) for t in T_]
S = [sorted(s) for s in S_]
cnt = 0
for _, g in groupby(sorted(T)):
if len(list(g))%2:
cnt += 1
if H%2 < cnt:
print("NO")
exit()
cnt = 0
for _, g in groupby(sorted(S)):
if len(list(g))%2:
cnt += 1
if W%2 < cnt:
print("NO")
exit()
if W%2 or H%2:
print("YES")
exit()
T1 = []
T2 = []
for i, (_, t) in enumerate(sorted(zip(T, T_))):
if i%2:
T1.append(t)
else:
T2.append(t)
T_p = T1 + T2[::-1]
S_pp = ["" for _ in range(W)]
for t in T_p:
for i, c in enumerate(t):
S_pp[i] += c
S1 = []
S2 = []
for i, (_, s) in enumerate(sorted(zip(S, S_pp))):
if i%2:
S1.append(s)
else:
S2.append(s)
S_p = S1 + S2[::-1]
for s1, s2 in zip(S_p, S_p[::-1]):
for c1, c2 in zip(s1, s2[::-1]):
if c1!=c2:
print("NO")
exit()
print("YES")
```
|
output
| 1
| 1,530
| 16
| 3,061
|
Provide a correct Python 3 solution for this coding contest problem.
There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.
Snuke can apply the following operation to this grid any number of times:
* Choose two different rows and swap them. Or, choose two different columns and swap them.
Snuke wants this grid to be symmetric. That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Constraints
* 1 \leq H \leq 12
* 1 \leq W \leq 12
* |S_i| = W
* S_i consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H
Output
If Snuke can make the grid symmetric, print `YES`; if he cannot, print `NO`.
Examples
Input
2 3
arc
rac
Output
YES
Input
3 7
atcoder
regular
contest
Output
NO
Input
12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv
Output
YES
|
instruction
| 0
| 1,531
| 16
| 3,062
|
"Correct Solution:
```
from collections import Counter
n,m = map(int,input().split())
grid = [list(input()) for i in range(n)]
def jc(a,b):
l = len(a)
used = [0]*l
for i in range(l):
if used[i]:
continue
for j in range(i+1,l):
if used[j]:
continue
if a[i] == b[j] and b[i] == a[j]:
used[i] = 1
used[j] = 1
break
if used.count(0) <= l%2:
return True
else:
return False
def judge(a):
h = len(a)
w = len(a[0])
used = [0]*h
for i in range(h):
if used[i]:
continue
ci = Counter(a[i])
for j in range(i+1,h):
if used[j]:
continue
cj = Counter(a[j])
if ci == cj:
if jc(a[i],a[j]):
used[i] = 1
used[j] = 1
break
if used.count(0) <= h%2:
return True
else:
return False
gt = list(zip(*grid))
if judge(grid) & judge(gt):
print("YES")
else:
print("NO")
```
|
output
| 1
| 1,531
| 16
| 3,063
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.
Snuke can apply the following operation to this grid any number of times:
* Choose two different rows and swap them. Or, choose two different columns and swap them.
Snuke wants this grid to be symmetric. That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Constraints
* 1 \leq H \leq 12
* 1 \leq W \leq 12
* |S_i| = W
* S_i consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S_1
S_2
:
S_H
Output
If Snuke can make the grid symmetric, print `YES`; if he cannot, print `NO`.
Examples
Input
2 3
arc
rac
Output
YES
Input
3 7
atcoder
regular
contest
Output
NO
Input
12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv
Output
YES
Submitted Solution:
```
import sys
from itertools import permutations
from random import randrange
readline = sys.stdin.readline
mod = 10**9+9
base = 2009
def rollinhash(S):
N = len(S)
has = 0
for i in range(N):
s = S[i]
has = (has*base + s)%mod
return has
phr = []
while len(set(phr)) != 26:
phr = [randrange(1, 10**9) for _ in range(26)]
def shash(S):
N = len(S)
has = 0
for i in range(N):
has = has + phr[S[i]]*phr[S[N-1-i]]
return has
H, W = map(int, readline().split())
G = [list(map(ord, readline().strip())) for _ in range(H)]
ans = 'NO'
fh = H//2
ch = H-fh
lir = list(range(H))
seen = set()
for k in permutations(lir, ch):
k = list(k)
sk = set(k)
for i in range(H):
if i not in sk:
k.append(i)
sh = shash(k)
if sh in seen:
continue
seen.add(sh)
G2 = []
for j in k:
G2.append(G[j])
G2 = list(map(list, zip(*G2)))
G2h = [rollinhash(g) for g in G2]
G2hi = [rollinhash(g[::-1]) for g in G2]
used = [False]*W
w1 = 0
match = W//2
while match and w1 < W:
if used[w1]:
w1 += 1
continue
sa = G2hi[w1]
for w2 in range(w1+1, W):
if used[w2]:
continue
if G2h[w2] == sa:
used[w1] = True
used[w2] = True
match -= 1
break
w1 += 1
if sum(used) >= W-1:
if sum(used) == W-1:
mid = used.index(False)
if G2h[mid] == G2hi[mid]:
ans = 'YES'
else:
ans = 'YES'
if ans == 'YES':
break
print(ans)
```
|
instruction
| 0
| 1,532
| 16
| 3,064
|
Yes
|
output
| 1
| 1,532
| 16
| 3,065
|
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