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;
    while(true){
        cin>>n>>k;
        if(n==0)break;
        vector<int> a(n+1,0);
        for (int i = 1; i <= n; ++i) {
            cin>>a[i];
            a[i]+=a[i-1];
        }
        int ans=0;
        for (int i = 0; i+k < n; ++i) {
            ans=max(ans,a[i+k]-a[i]);
        }
        cout<<ans<<endl;
    }
    return 0;
}
