Zero Sum Subarray of Fixed Length

Given an array of integers and an integer n, determine whether there exists a contiguous subarray of length n whose sum equals 0.

In other words, given an array \( arr \) of length \( m \) and an integer \( n \), check if there exists an index \( i \) (with \( 0 \le i \le m - n \)) such that \[ \sum_{j=i}^{i+n-1} arr[j] = 0 \]

If such a subarray exists, print True; otherwise, print False.

inputFormat

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

1. The first line contains two space-separated integers \( m \) and \( n \), where \( m \) is the length of the array and \( n \) is the required subarray length.
2. The second line contains \( m \) space-separated integers representing the array elements.

outputFormat

Output to standard output (stdout) a single line containing either True or False depending on whether a contiguous subarray of length n with sum equal to \( 0 \) exists.

7 3
1 2 -3 4 -2 2 1

True