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 sc = new Scanner(System.in);
		
		while(true){
			final int n = sc.nextInt();
			final int k = sc.nextInt();
			
			if(n == 0 && k == 0){
				break;
			}
			
			int[] array = new int[n];
			
			for(int i = 0; i < n; i++){
				array[i] = sc.nextInt();
			}
			
			int sum = 0;
			for(int i = 0; i < k; i++){
				sum += array[i];
			}
			
			int max = sum;
			for(int i = 0, m = k; m < n; i++, m++){
				sum += array[m] - array[i];
				max = Math.max(sum, max);
			}
			
			System.out.println(max);
		}
		
	}
}