| *This problem shares some similarities with B2, with key differences in bold.* |
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| Given a positive integer \(P\), please find an array of at most \(100\) positive integers which have a sum of \(41\) and a product of \(P\), or output \(-1\) if no such array exists. |
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| If multiple such arrays exist, **you may output any one of them**. |
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| # Constraints |
| \(1 \leq T \leq 965\) |
| \(1 \leq P \leq 10^9\) |
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| # Input Format |
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| Input begins with an integer \(T\), the number of test cases. For each case, there is one line containing a single integer \(P\). |
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| # Output Format |
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| For the \(i\)th test case, if there is no such array, print "`Case #i: -1`". Otherwise, print "`Case #i:` " followed by the integer \(N\), the size of your array, followed by the array itself as \(N\) more space-separated positive integers. |
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| # Sample Explanation |
| In the first sample, we must find an array with product \(2023\), and sum \(41\). One possible answer is \([7, 17, 17]\). |
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