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;
	
	while(scanf("%d%d",&n,&k),n,k){
		int max=0,temp=0;
		int val[100000]={0};
		
		for(i=0;i<n;i++){
			scanf("%d",&val[i]);
			temp+=val[i];
			if(i>=k)temp-=val[i-k];
			if(i>k-1 && temp>max)max=temp;
		}
		
		printf("%d\n",max);
		
	}
	return 0;
}