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>

using namespace std;

int main()
{
	int n, k;
	while (scanf("%d %d", &n, &k), n || k) {
		int N[100001];

		for (int i = 1; i <= n; ++i) scanf("%d", &N[i]);

		int sum = 0;

		for (int i = 1; i <= k; ++i) sum += N[i];

		int a = sum;

		for (int i = k; i < n; ++i) {
			a += N[i+1] - N[i-k+1];
			sum = sum > a ? sum : a;
		}

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