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.*;
import static java.lang.System.*;

public class Main {

	Scanner sc = new Scanner(in);
	
	void run() {
		int[] a = new int[100001];
		while (true) {
			int n = sc.nextInt(), k = sc.nextInt();
			if (n == 0 && k == 0) break;
			for (int i = 0; i < n; i++)
				a[i] = sc.nextInt();
			int max = 0;
			for (int i = 0; i < k; i++)
				max += a[i];
			int sum = max;
			for (int i = 0; i < n-k; i++) {
				sum = sum - a[i] + a[i+k];
				max = Math.max(max, sum);
			}
			out.println(max);
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}

}