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.*;

public class Main{
	public static void main(String[] args){
		int i,j;
		int pre,max;
		Scanner sc = new Scanner(System.in);

		while(true){
			int n=sc.nextInt(), k=sc.nextInt();
			if(n==0 && k==0) break;
			int[] x = new int[n];

			for(i=0;i<n;i++) x[i]=sc.nextInt();
			for(i=0,pre=0;i<k;i++) pre+=x[i];
			max = pre;
			for(j=1;j<n-k;j++){
				pre = pre - x[j-1] + x[k+j-1];
				if(max < pre) max = pre;
			}
			System.out.println(max);
		}
	}
}