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>
using namespace std;

int main()
{
	int n,k;

	int suu[100000 + 100] = { 0 };
	int a;
	int i;
	int mx;

	cin >> n >> k;

	while (n != 0 && k != 0)
	{
		for (i = 1; i <= n; i++)
		{

			cin >> a;

			suu[i] = a + suu[i - 1];

		}

		for (i = k; i <= n; i++)
		{
			if (mx < suu[i] - suu[i - k])
			{
				mx = suu[i] - suu[i - k];
			}

		}

		cout << mx << endl;


		cin >> n >> k;
		mx = 0;
	}
	return 0;
}