Subset Rope Selection

You are given n ropes with various lengths and a target length m. Your task is to determine whether there exists a subset of these ropes such that their total length is exactly m meters.

The problem can be formally stated as follows:

Find a subset S of the set of ropes such that \[ \sum_{i \in S} a_i = m, \] where \(a_i\) is the length of the i-th rope.

If such a subset exists, output YES; otherwise, output NO.

inputFormat

The input is read from standard input and consists of two lines:

• The first line contains two space-separated integers n and m, where n (1 ≤ n ≤ 20) is the number of ropes and m is the target length in meters.
• The second line contains n space-separated integers representing the lengths of the ropes.

outputFormat

Output a single line to standard output: YES if there exists a subset of ropes whose total length equals m, otherwise output NO.

4 10
2 3 7 9

YES