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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;

public class Main{
	public static void main(String[] args)throws IOException{
		InputStreamReader isr = new InputStreamReader(System.in);
		BufferedReader reader = new BufferedReader(isr);
		String string;
		int n, m, max, hoge, array[];
		
		while(!(string = reader.readLine()).equals("0 0")){
			n = Integer.valueOf(string.split(" ")[0]);
			m = Integer.valueOf(string.split(" ")[1]);
			
			array = new int[n];
			for(int i = 0; i < n; i++) array[i] = Integer.valueOf(reader.readLine());
			
			max = 0;
			for(int i = 0; i < n - m + 1; i++){
				hoge = 0;
				for(int j = i; j < i + m; j++) hoge += array[j];
				if(hoge > max) max = hoge;
			}
			
			System.out.println(max);
		}
		
		reader.readLine();
	}
}