2023/round1/sum_41_ch2.md

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]).