Minimum Partition Difference

Given a list of integers, your task is to partition it into two non-empty subsets such that the absolute difference between the sums of the two subsets is minimized.

You need to output three integers separated by a space: the minimum absolute difference, the sum of one subset, and the sum of the other subset.

The absolute difference is defined as \( |S_1 - S_2| \), where \( S_1 \) and \( S_2 \) are the sums of the two subsets respectively.

Note: It is guaranteed that a valid partition exists for each test case.

inputFormat

The input is read from stdin and is formatted as follows:

1. The first line contains an integer \( T \), the number of test cases.
2. For each test case, the first line contains an integer \( n \), the number of elements in the list.
3. The second line contains \( n \) space-separated integers.

outputFormat

For each test case, output a single line to stdout containing three space-separated integers: the minimum absolute difference, the sum of one subset, and the sum of the other subset.

1
5
7 3 2 5 8

1 12 13