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A polynomial in `x` of degree **D** can be written as: |
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aDxD + aD-1xD-1 + ... + a1x1 + a0 |
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In some cases, a polynomial of degree `**D**` can also be written as the |
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product of two polynomials of degrees `**D1**` and `**D2**`, where `**D = D1 |
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\+ D2**`. For instance, |
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4 x2 + 11 x 1 + 6 = (4 x1 + 3) * (1 x1 + 2) |
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In this problem, you will be given two polynomials, denoted `**F**` and |
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`**G**`. Your task is to find a polynomial `**H**` such that `**G** * **H** = |
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**F**`, and each `ai` is an integer. |
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## Input |
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You should first read an integer `**N ≤ 60**`, the number of test cases. Each |
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test case will start by describing `**F**` and then describe `**G**`. Each |
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polynomial will start with its degree `0 ≤ **D** ≤ 20`, which will be followed |
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by `**D**+1` integers, denoting `a0, a1, ... , aD`, where `-10000 ≤ ai ≤ |
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10000`. Each polynomial will have a non-zero coefficient for it's highest |
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order term. |
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## Output |
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For each test case, output a single line describing `**H**`. If `**H**` has |
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degree `**DH**`, you should output a line containing `**DH** \+ 1` integers, |
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starting with `a0` for `**H**`. If no `**H**` exists such that `**G*H=F**`, |
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you should output "no solution". |
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