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,a[100000],temp;
	while(cin >> n >> k,n || k){
		cin >> a[0];
		for(int i = 1;i < n;i++){
			cin >> temp;
			a[i] = a[i - 1] + temp;
		}
		temp = 0;
		for(int i = 0;i < n - k;i++)
			if(temp < a[i + k] - a[i])
				temp = a[i + k] - a[i];
		cout << temp << endl;
	}
	return 0;
}