| Operators |
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| - You are given n operators op₁, op₂, …, opₙ. For an input sequence of |
| n+1 integers a₀, a₁, …, aₙ, you need to compute the following value: |
| (((…(a₀ op₁ a₁) op₂ a₂) op₃ a₃)… opₙ aₙ) mod (10⁹ + 7). |
| - For any 0 ≤ i ≤ n, we have 0 ≤ aᵢ < 10⁹ + 7. |
| - For any 1 ≤ i ≤ n, opᵢ ∈ {+, ×}; that is, each operator is either |
| addition “+” or multiplication “×”. |
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| You quickly wrote a program to solve this problem. Unfortunately, |
| because you were over‑excited after solving it, you accidentally deleted |
| the original problem statement and your code. As a result, you lost the |
| information about the n operators op₁, …, opₙ. Fortunately, you still |
| have the program you just compiled, so you can recover these operators |
| by querying your program. |
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| Since the contest is about to end, and the program you wrote is not |
| efficient enough, you cannot ask more than Qₘₐₓ = 600 queries. |
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| Implementation details |
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| This is an interactive problem. As usual, you should submit a source code file that can compile. |
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| Initially, you should read an integer n, the number of operators. |
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| You may issue queries by writing to standard output lines of the form |
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| ? a₀ a₁ … aₙ |
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| 1 <= a_i < 10^9+7 |
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| Then you must flush output, and read from standard input one integer in [0, 10⁹ + 6], representing the interactor’s response. |
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| When you have determined the operators, output a line of the form |
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| ! o₁ o₂ … oₙ |
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| o_i is 0 if op_i is "+", is 1 if op_i is "×". |
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| Remember to flush after your output. |
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| Subtasks |
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| - For all data, 1 ≤ n ≤ 600. |
| - Let your program make Q queries: |
| - If your program exceeds time limit, memory limit, or returns |
| incorrect answer → score=0. |
| - Otherwise, your score depends on Q: |
| - score(Q) = 41 / (Q + 1) |
| - In other words, a solution with Q ≤ 40 is awarded the full score. |
