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
#include <stdio.h>
int main(){
	for(;;){
		int max=0,set[100000],n,m,a,b,c;
		scanf("%d%d",&n,&m);
		if(n==0&&m==0)
		break;
		for(a=0;a<n;a++){
			scanf("%d",&set[a]);
		}
		for(a=0;a<n-m;a++){
			c=0;
			for(b=0;b<m;b++){
				c+=set[a+b];
			}
			if(max<c)
			max=c;
		}
		printf("%d\n",max);
	}
	return 0;
}