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>
#include<algorithm>
using namespace std;
#pragma warning(disable:4996)
long long n, k, a[200000], s, ret;
int main() {
	while (true) {
		cin >> n >> k; s = 0; if (n == 0)break; for (int i = 1; i <= n; i++) { scanf("%lld", &a[i]); if (i <= k)s += a[i]; }
		ret = s; for (int i = k + 1; i <= n; i++) { s -= a[i - k]; s += a[i]; ret = max(ret, s); }
		cout << ret << endl;
	}
	return 0;
}