Problem D
Equal Sums (Easy)
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).
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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.
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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. $1 \leq T \leq 10$. $N$ is exactly equal to 20. Each number in $S$ will be a positive integer less than $10^{5}$.
| Sample Input 1 | Sample Output 1 |
|---|---|
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 |
Case #1: 1 2 3 Case #2: 3117 4210 4943 2328 2894 7048 |
