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<vector>
#include<string>
#include<map>
using namespace std;

int main() 
{
	int n = -100000;
	int a, b;
	while (cin >> a >> b, a || b) {
		vector<int>s(a);
		for (int c = 0; c < a; c++)cin >> s[c];
		int m = 0;
		for (int e = 0; e < b; e++) {
			m += s[e];
		}
		if (n < m)n = m;
		for (int d = 0; d < a - b; d++) {
			m -= s[d];
			m += s[d + b];
			if (n < m)n = m;
		}
		cout << n << endl;
	}
}