problem

Given a sequence of n integers a1, a2, ..., an and a positive integer k (1 ≤ k ≤ n), then the sum of k consecutive integers Si = ai + ai + Create a program that outputs the maximum value of 1 + ... + ai + k-1 (1 ≤ i ≤ n --k + 1).



input

The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.

On the first line, the positive integer n (1 ≤ n ≤ 100000) and the positive integer k (1 ≤ k ≤ n) are written in this order, separated by blanks. The first + i lines after the second line. (1 ≤ i ≤ n) contains the i-th term ai (-10000 ≤ ai ≤ 10000) in the sequence. Of the scoring data, 60% of the points are n ≤ 5000, k ≤ 1000. Meet.

The number of datasets does not exceed 5.

output

The maximum value of Si is output to one line for each data set.

Examples

Input

5 3
2
5
-4
10
3
0 0


Output

11


Input

None


Output

None
import java.util.Scanner;
public class Main{

	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);

		while(true) {
		int n = stdIn.nextInt();
		int k = stdIn.nextInt();
		
		if(n==0)break;
		int[] a = new int[n];
		for(int i = 0; i < n; i++) {
			a[i] = stdIn.nextInt();
		}
		
		int[] s = new int[n+1];
		s[0] = 0;
		
		for(int i = 0; i < n; i++) {
			s[i+1] = s[i]+a[i];
		}
		
		long ans = Long.MIN_VALUE;
		
		for(int i = 0; i <=n-k; i++) {
			long val = s[k+i] - s[i];
			if(ans < val) ans = val;
		}
		
		System.out.println(ans);
		
		}
		
		
	}

}

