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.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] = sc.nextInt();
            }

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

            int ans = 0;
            int tmp = 0;
            for(int i=0; i<=n-k; i++) {
                tmp = s[i+k] - s[i];
                if(ans < tmp) {
                    ans = tmp;
                }
            }
            System.out.println(ans);
        }
    }
}

