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.*;
public class Main {

	public void doIt(){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		while(!(n == 0 && k == 0)){
			int [] list = new int[n];
			list[0] = sc.nextInt();
			for(int i=1; i < n; i++){
				list[i] = list[i-1] + sc.nextInt();
			}
			int max = list[k-1];
			for(int i=1; i + k - 1 < n; i++){
				int result = list[i+k-1] - list[i-1];
				if(result > max){
					max = result;
				}
			}
			System.out.println(max);

			n = sc.nextInt();
			k = sc.nextInt();
		}
	}
	public static void main(String[] args) {
		Main obj = new Main();
		obj.doIt();

	}

}