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;
long su[100000010] = { 0 };
long sai;
int main()
{
	long n, k;
	long i, j;
	long a;
	while (cin >> n >> k, n != 0 && k != 0)
	{
		for (i = 1; i <= n; i++)
		{
			cin >> a;
			su[i] = su[i - 1] + a;
		}
		sai = 0;
		for (i = k; i <= n; i++)
		{
			if (sai < su[i] - su[i - k])
			{
				sai = su[i] - su[i - k];
			}
		}
		cout << sai << endl;
	}
	return 0;
}