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 <bits/stdc++.h>
using namespace std;

int main() {
    int n,k,i,ans=0;
    cin >> n >> k;
    while(n!=0 || k!=0){
        int a,sum[1000000],S;
        sum[0]=0;
    
        for(i=0;i<n;++i){
            cin >> a;
            sum[i+1] = sum[i] + a;
        }
    
        for(i=0;i<n-k;++i){
            S=sum[i+k]-sum[i];
            ans = max(ans,S);
        }
    
        cout << ans << endl;
        cin >> n >> k;
    }
}

