| *This problem shares some similarities with B1, with key differences in bold.* | |
| 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. | |
| If multiple such arrays exist, **print one with the fewest number of elements**. If there are multiple with the fewest number of elements, you may print any one of them. | |
| # Constraints | |
| \(1 \leq T \leq 960\) | |
| \(1 \leq P \leq 10^9\) | |
| # Input Format | |
| Input begins with an integer \(T\), the number of test cases. For each case, there is one line containing a single integer \(P\). | |
| # Output Format | |
| 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. | |
| # Sample Explanation | |
| In the first sample, we must find an array with product \(2023\), and sum \(41\). One possible answer is \([7, 17, 17]\). | |