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) {
				break;
			}
			int[] sum = new int[n+1];
			for(int i=1;i<=n;i++) {
				sum[i] = sum[i-1] + sc.nextInt();
			}
			int ans = 0;
			for(int i=1;i<=n-k+1;i++) {
				ans = max(ans,sum[i+k-1]-sum[i-1]);
			}
			System.out.println(ans);
		}
		sc.close();
	}
	static private int max(int a, int b) {
		return a > b ? a : b;
	}
}