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<algorithm>
#include<string>
#include <vector>

using namespace std;

int main(){

	int n,k,a[100000],sum,ans,i;

	while(cin>>n>>k,n||k){

	sum=0;

	for(i=0;i<n;i++){
		cin>>a[i];
	}

	for(i=0;i<k;i++){
		sum=sum+a[i];
	}

    ans=sum;
    i=0;

    for(i=k;i<n;i++){
    	sum=sum-a[i-k]+a[i];
    	ans=max(ans,sum);
    }

    cout<<ans<<endl;
	}
}