Equal Sum Partition

You are given a list of positive integers. Your task is to determine whether the list can be partitioned into two subsets such that the sum of elements in both subsets is equal.

Formally, given an array \( nums \), decide if there exists two disjoint subsets \( A \) and \( B \) such that \( A \cup B = nums \) and \( \sum_{a \in A}a = \sum_{b \in B}b \). If such a partition exists, output YES; otherwise, output NO.

Hint: The total sum must be even to allow an equal partition. Use a dynamic programming approach to check if a subset with sum equal to half of the total sum exists.

inputFormat

The input is read from stdin and consists of multiple lines. The first line contains a single integer \( T \) representing the number of test cases. Each of the following \( T \) lines contains a space-separated list of positive integers.

outputFormat

For each test case, output a single line to stdout that is either YES if the list can be partitioned into two subsets with equal sum, or NO otherwise.

2
1 5 11 5
1 2 3 5

YES
NO