Maximum Sum Subarray of Fixed Length

You are given an array of N integers and an integer M representing the size of a subarray. Your task is to find the maximum sum of any contiguous subarray of length exactly M.

The problem can be formally stated as follows: Given an array \(A\) of length \(N\) and an integer \(M\), find the maximum value of the sum: \[ S = \sum_{i=k}^{k+M-1} A_i \] for all valid indices \(k\) such that \(0 \leq k \leq N-M\).

Input Format: The first line contains two integers \(N\) and \(M\). The second line contains \(N\) space-separated integers representing the array \(A\).

Output Format: Print a single integer which is the maximum sum of any contiguous subarray of length \(M\).

Example:

Input:
5 3
2 1 5 1 3
Output:
9

inputFormat

The first line contains two integers N and M separated by a space. The second line contains N integers separated by spaces representing the array A.

outputFormat

A single integer which is the maximum sum of any contiguous subarray of length M.## sample

5 3
2 1 5 1 3

9