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 in=new Scanner(System.in);
		for(;;)
		{
			int n=in.nextInt(),k=in.nextInt();
			int a[]=new int[n];
			int pre=0;
			if((n|k)==0)
				return;
			for(int i=0;i<n;i++)
				a[i]=in.nextInt();
			for(int i=0;i<k;i++)
				pre+=a[i];
			int max=pre;
			
			for(int i=0;i<n-k;i++)
			{
				pre=pre-a[i]+a[k+i];
				max=Math.max(max, pre);
			}
			System.out.println(max);
		}
	}
}