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 <algorithm>
#include <vector>

using namespace std;

int main(void){
	int n, k, t, m;
	while(true){
		scanf("%d %d", &n, &k);

		if(n == 0 && k == 0) return 0;

		vector<int> a;

		for(int i = 0;i < n;++i){
			scanf("%d", &t);
			a.push_back(t);
		}

		m = 0;
		for(int i = 0;i < n-k;++i){
			t = 0;
			for(int j = 0;j < k;++j){
				t += a[i+j];
			}
			m = max(m, t);
		}

		printf("%d\n", m);
	}
}
