Subarray Sum Existence

You are given an array of non-negative integers and a target sum k. Your task is to determine whether there exists a contiguous subarray whose sum is exactly k.

The efficient solution to this problem uses a sliding window technique. In this method, we maintain a window with indices \(start\) and \(end\) and a running sum \(S = a_{start} + a_{start+1} + \cdots + a_{end}\). We adjust this window so that \(S\) approaches the target value \(k\). If at any point \(S = k\), output True; otherwise, after processing the array, output False.

Note: When the array is empty, the output should be False.

inputFormat

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

• The first line contains two integers n and k separated by a space, where n is the number of elements in the array and k is the target sum.
• The second line contains n non-negative integers separated by space representing the array. If n is 0, the second line will be empty.

outputFormat

Output a single line to standard output (stdout) containing either True if there exists a contiguous subarray whose sum is exactly k, or False if no such subarray exists.

5 12
1 2 3 7 5

True