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<bits/stdc++.h>

using namespace std ;

int main()
{
	int n ;
	while( cin >> n ,n )
	{
		int m ;
		cin >> m ;
		int num[ n ] ;
		for( int i  = 0 ; i < n ; i++ )
			cin >> num[ i ] ;
		int ans = 0 ;
		for( int i  = 0 ; i < n ; i++ )
		{
			int cnt = 0 ;
			for( int j = i ; j < m + i && m + i < n ; j++ )
				cnt += num[ j ] ;
			ans = max( ans ,cnt ) ;
		}
		cout << ans << endl ;
	}
	return 0 ;
}