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 <cstdint>
#include <algorithm>
#include <cstring>

std::int64_t a[100000];

int main() {
	int n, k;
	while (std::cin >> n >> k, n + k != 0) {
		for (int i = 0; i < n; ++i)
			std::cin >> a[i];

		std::int64_t res = 0, mem = 0;
		for (int i = 0; i < n; ++i) {
			mem += a[i];

			if (i >= k) {
				mem -= a[i - k];
				res = std::max(res, mem);
			}
		}

		std::cout << res << std::endl;
	}
}