Subset Sum Existence

You are given a multiset of n positive integers and an integer x. Your task is to determine whether there exists a non-empty subset of the multiset whose sum is exactly x. Note that each number in the multiset may be used at most once.

Input Constraints:

• 1 ≤ n ≤ 10⁵ (for example)
• 1 ≤ x ≤ 10⁹ (for example)
• Each element of the multiset is a positive integer.

Hint: Use dynamic programming. In particular, define a boolean DP array where \(dp[s]\) is true if there is a subset with sum \(s\). The recurrence can be written as:

\[ \text{dp}[s] = \text{dp}[s] \vee \text{dp}[s - a_i] \quad \text{for each } a_i \text{ in the multiset, with } s \geq a_i. \]

inputFormat

The first line contains two integers n and x, where n is the number of elements in the multiset and x is the target sum.

The second line contains n space-separated positive integers, representing the multiset.

outputFormat

Print a single line containing YES if there is a non-empty subset of the multiset that sums to x; otherwise, print NO.

## sample

5 9
2 2 3 5 3

YES

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