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>
#include<string.h>
#include<algorithm>
using namespace std;
int main(void){
	int a[100001];
	int n,k,sum,t;
	for(;;){
		scanf("%d%d",&n,&k);
		if(n==0&&k==0)return 0;
		sum=t=0;
		for(int i=0;i<n;i++){
			scanf("%d",a+i);
			t+=a[i];
			if(i>=k){
				t-=a[i-k];
				sum=max(sum,t);
			}
			//printf("t %d\n",t);
		}
		printf("%d\n",sum);
	}
}