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 scanner = new Scanner(System.in);
		int sum, max_sum;
		int num, c_num;
		int [] number = new int[100000];
		
		num = scanner.nextInt();
		c_num = scanner.nextInt();
		while(num != 0 || c_num != 0) {
			sum = max_sum = 0;
			
			for(int i = 0; i < num; i++) {
				number[i] = scanner.nextInt();
			}
			
			for(int i = 0; i < c_num; i++) {
				sum += number[i];
			}
			max_sum = sum;
			
			for(int i = 1; i < num - c_num + 1; i++) {
				sum -= number[i - 1];
				sum += number[i + c_num - 1];
				if (sum > max_sum ) {
					max_sum = sum;
				}
			}

			System.out.println(max_sum);
			
			num = scanner.nextInt();
			c_num = scanner.nextInt();
		}
	}
}