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 <vector>
using namespace std;

int main() {
	
	while(true){
	int n,k;
	cin >> n >> k;
	if(n==0&&k==0)break;
	
	vector<int> s(n);
	for(int i=0;i<n;i++){
		cin >> s[i];
	}
	int sum=0;
	for(int i=0;i<k;i++){
		sum+=s[i];
	}
	int ans = sum;
	for(int i=0;i+k<n;i++){
		sum+=s[i+k]-s[i];
		if(sum>ans)ans=sum;
	}
	cout << ans << endl;
	}
	
	return 0;
}