Contiguous Subarray Sum

You are given an array of n integers and a target value k. Your task is to determine whether there exists a contiguous subarray whose sum is equal to k.

This problem can be approached using prefix sums. Recall that the cumulative sum at index \(i\) is defined as \(S_i = a_1 + a_2 + \dots + a_i\). Using a hash map to store the prefix sums, you can check if there is an index j such that \(S_i - S_j = k\), which indicates that the subarray from index j+1 to i sums to k.

Try to design an efficient solution that runs in linear time.

inputFormat

The input is given via standard input (stdin) and consists of two lines:

• The first line contains two space-separated integers: n (the number of elements in the array) and k (the target sum).
• The second line contains n space-separated integers representing the elements of the array.

outputFormat

Output a single line to standard output (stdout) with the string YES if a contiguous subarray whose sum is equal to k exists; otherwise output NO.

5 15
1 2 3 4 5

YES