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>
#define INF 2000000000
using namespace std;

int main(){
	int n,k,a[100001];
	while(1){
		a[0] = 0;
		cin >> n >> k;
		if(n == 0 && k == 0) break;
		for(int i = 0;i < n;i++) {
			int t;
			cin >> t;
			a[i + 1] = a[i] + t;
		}
		int ma = -INF;
		for(int i = 0;i <= n - k;i++){
			ma = max(ma,a[i + k] - a[i]);
		}
		cout << ma << endl;
	}
	return 0;	
}