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(void){
	for (;;){
	int a,b,c[100000]={0},d=0,e=0,max=0;
			cin>>a>>b;
			if (a==0&&b==0)break;
			for (int A=0;A<a;A++){
			cin>>c[A];
			if (A>=b){
				for (int B=0;B<b;B++){
					d=d+c[A+e];
					e--;
				}
				if (max<d)max=d;
				d=0;
				e=0;
			}
		}
		cout<<max<<endl;
	}
	return 0;
}