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 <climits>

int main() {
    using namespace std;
    
    int n, k;
    while(cin >> n >> k, (n|k)) {
        int arr[n]; cin >> arr[0]; for(int i=1; i<n; i++) { cin >> arr[i]; arr[i] += arr[i-1]; }
    
        int res = INT_MIN/4;

        for(int i=0; i<n-k; i++) {
            res = max(res, arr[i+k]-arr[i]);    
        }
    
        cout << res << endl;
    }
    
    return 0;
}