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;

int main( void )
{
	int n, k, input[100000];
	while(cin >> n >> k, n | k) {
		int sum = 0;
		for(int i=0; i < n; ++i) {
			cin >> input[i];
			if(i < k) sum += input[i];
		}
		int i, j, ans = sum;
		i = 0; j = k-1;
		while(j < n-1) {
			sum -= input[i++];
			sum += input[++j];
			ans = max(ans, sum);
		}
		cout << ans << endl;
	}
	return 0;
}