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 <cmath>
#include <cstdio>
using namespace std;
int n, k;
int a[1000000];
int s, t;
int main()
{
	cin >> n >> k;
	while(n*k!=0)
	{
		s=0;
		for(int i=0; i<k; i++)
		{
			cin >> a[i];
			s+=a[i];
			t=s;
		}
		for(int i=k; i<n; i++)
		{
			cin >> a[i];
			t=t+a[i]-a[i-k];
			s=max(s, t);
		}
		cout << s << endl;
		cin >> n >> k;
	}
	return 0;
}