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 {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        while (true) {
            int n = sc.nextInt();
            int k = sc.nextInt();

            if (n == 0 && k == 0) break;

            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = Integer.parseInt(sc.next());

            int[] s = new int[n + 1];
            s[0] = 0;
            for (int i = 0; i < n; i++) s[i+1] = s[i] + a[i];

            long ans = Long.MIN_VALUE;
            for (int i = 0; i <= n-k; i++) {
                long val = s[i+k] - s[i];
                if (ans < val) ans = val;
            }

            System.out.println(ans);
        }
    }
}

