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>

long long int re[100001];

int main(){
	int n,k,i;
	long long c;
	re[0]=0;
	while(0<=scanf("%d%d",&n,&k)){
		if(n==0 && k==0)break;
		
		for(i=1;i<=n;i++){
			scanf("%lld",&c);
			re[i]=re[i-1]+c;
		}
		c=re[k];
		for(i=1;i+k-1<=n;i++){
			if(c<re[i+k-1]-re[i-1])c=re[i+k-1]-re[i-1];
		}
		printf("%lld\n",c);
	}
	return 0;
}