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>
#include <algorithm>
#pragma warning(disable : 4996)
using namespace std;
int n, m, a[100009];
int main() {
	while (scanf("%d%d", &n, &m), n) {
		for (int i = 0; i < n; i++) scanf("%d", &a[i]);
		int sum = 0;
		for (int i = 0; i < m; i++) sum += a[i];
		int ret = sum;
		for (int i = m; i < n; i++) {
			sum += a[i] - a[i - m];
			ret = max(ret, sum);
		}
		printf("%d\n", ret);
	}
	return 0;
}