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 static void main(String[] args) 
	{
		Scanner stdIn = new Scanner(System.in);
		while(stdIn.hasNext())
		{
			int n = stdIn.nextInt();
			int k = stdIn.nextInt();
			if(n == 0 && k == 0)
			{
				break;
			}
			List<Integer> list = new ArrayList<Integer>();
			for(int i = 0; i < n; ++i)
			{
				int a = stdIn.nextInt();
				list.add(a);
			}
			int max = 0;
			int sum = 0;
			for(int i = 0; i < k; ++i)
			{
				sum += list.get(i);
			}
			if(max < sum)
			{
				max = sum;
			}
			for(int i = 1; i + k - 1 < n; ++i)
			{
				sum -= list.get(i - 1);
				sum += list.get(i + k - 1);
				if(max < sum)
				{
					max = sum;
				}
			}
			System.out.println(max);
		}
	}
}