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

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    void run() {
        Scanner sc = new Scanner(System.in);
        for (;;) {
            int n = sc.nextInt(), k = sc.nextInt();
            if ((n|k) == 0) break;
            int[] ar = new int[n];
            for (int i = 0; i < n; i++) {
                ar[i] = sc.nextInt();
            }
            
            int sum = 0;
            for (int i = 0; i < k; i++) {
                sum += ar[i];
            }
            int ans = sum;
            for (int i = k; i < n; i++) {
                sum += ar[i] - ar[i - k];
                ans = Math.max(ans, sum);
            }
            
            System.out.println(ans);
        }
    }
        
    void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }
    
    public static void main(String[] args) {
        new Main().run();
    }
}