2023/round1/sum_41_ch1.md

This problem shares some similarities with B2, 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, you may output any one of them.

Constraints

(1 \leq T \leq 965) (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]).