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(void){
	int i,n,k,sum,max;
	int N[150000];

	while(0==0){
		scanf("%d %d",&n,&k);
		sum=0;
		if(n==0 && k==0) break;

		for(i=0;i<n;i++)
			scanf("%d",&N[i]);

		for(i=0;i<k;i++)
		    sum+=N[i];
		
		max=sum;

		for(i=k;i<n;i++){
			sum+=N[i];
			sum-=N[i-k];
			if(sum>max)max=sum;
		}

		printf("%d\n",max);
	}
	return 0;
}