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.*;

class Main {
        public static void main(String args[]) {
                Scanner sc = new Scanner(System.in);
                while(true) {
                        Integer N = sc.nextInt();
                        Integer K = sc.nextInt();
                        if (N == 0 && K == 0) {
                                break;
                        }
                        Integer[] a = new Integer[N];

                        Long ans = Long.MIN_VALUE;
                        for (Integer i = 0; i < N; i++) {
                                a[i] = sc.nextInt();
                                if (i != 0) {
                                        a[i] += a[i-1];
                                }
                                if (i >= K) {
                                        ans = Math.max(a[i] - a[i - K], ans);
                                }
                        }
                        System.out.println(ans);
                }
        }
}