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;

//Maximum Sum
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 = 0;
			int t = 0;
			int tmp = 0;
			while(t < k){
				tmp += a[t];
				t++;
			}
			int max = tmp;
			while(t < n){
				tmp -= a[s++];
				tmp += a[t++];
				max = Math.max(max, tmp);
			}
			System.out.println(max);
		}
	}
}