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 <cstdio>

int main(){
	int a[100001], n, k, max;
	while(scanf("%d %d", &n, &k), n || k){
		max = 0;
		for(int i = 0;i < n;i++)scanf("%d", &a[i]);
		for(int i = 0;i < k;i++)max += a[i];
		for(int i = 1;i < n-k+1;i++){
			int s = 0;
			for(int j = i;j < i+k;j++)s += a[j];
			if(s > max)max = s;
		}
		printf("%d\n", max);
		}
	return 0;
}