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 <cstdio>
#include <vector>
using namespace std;
int main() {
	int n, k;
	while (scanf("%d %d",&n,&k)&&n!=0) {
		vector<int> a(n);
		for (int i=0; i<n; i++) scanf("%d",&a[i]);
		int max=0;
		for (int i=0; i<k; i++) max+=a[i];
		int tmp=max;
		for (int i=0; i<n-k; i++) {
			tmp=tmp-a[i]+a[i+k];
			if (tmp>max) max=tmp;
		}
		printf("%d\n",max);
	}
}