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<iostream>
using namespace std;
int n2[100001];
int main() {
	int n, k;
	int cnt = 0, cnt_max = -10001;
	while (1) {
		cin >> n >> k;
		if (n == 0 && k == 0)return 0;
		for (int i = 1; i <= n; i++) {
			cin >> n2[i];
		}
		for (int i = 1; i <= n - k + 1; i++) {
			cnt = n2[i];
			for (int j = 1; j < k; j++) {
				cnt += n2[i + j];
			}
			if (cnt_max < cnt) {
				cnt_max = cnt;
			}
		}
		cout << cnt_max << endl;
		cnt_max = 0;
	}
}