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 n,k;
int a[100000];
int r,l;
int m,t;
int i,j;

int max(int a,int b){
	if(a>=b)return a;
	else return b;
}

int main(){
	while(1){
		scanf("%d %d",&n,&k);
		if(n==0&&k==0)return 0;
		for(i=0;i<n;i++)scanf("%d",&a[i]);
		r=0;l=k-1;
		m=0;
		for(i=0;i<k;i++){
			m+=a[i];
			t=m;
		}
		while(l<n-1){	
			t+=a[++l];
			t-=a[r++];
			m=max(m,t);
		}
		printf("%d\n",m);
	}
}
		