 Equal Sums

Round 1B, 2012

Submit Solution(Code Jam Page)

Problem

I have a set of positive integers S. Can you find two non-empty, distinct subsets with the same sum?

Note: A subset is a set that contains only elements from S, and two subsets are distinct if they do not have exactly the same elements.

Input

The first line of the input gives the number of test cases, T. T test cases follow, one per line. Each test case begins with N, the number of positive integers in S. It is followed by N distinct positive integers, all on the same line.

Output

For each test case, first output one line containing "Case #x:", where x is the case number (starting from 1).

• If there are two different subsets of S that have the same sum, then output these subsets, one per line. Each line should contain the numbers in one subset, separated by spaces.
• If it is impossible, then you should output the string "Impossible" on a single line.
If there are multiple ways of choosing two subsets with the same sum, any choice is acceptable.

Limits

No two numbers in S will be equal.
1 ≤ T ≤ 10.

Small dataset

N is exactly equal to 20.
Each number in S will be a positive integer less than 105.

Large dataset

N is exactly equal to 500.
Each number in S will be a positive integer less than 1012.

Sample

 Input 2 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 120 266 858 1243 1657 1771 2328 2490 2665 2894 3117 4210 4454 4943 5690 6170 7048 7125 9512 9600 Output Case #1: 1 2 3 Case #2: 3117 4210 4943 2328 2894 7048

Points Correct Attempted
6pt 2257 2531
37pt 149 853

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