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.File;
import java.io.FileNotFoundException;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws FileNotFoundException {

		Scanner scan = new Scanner(System.in);
		// Scanner scan = new Scanner(new File("c:\\0515-input.txt"));
		while (true) {
			int n = scan.nextInt();
			int k = scan.nextInt();
			if (n == 0 & k == 0)
				break;

			int[] e = new int[k];
			int max = 0;
			for (int i = 0; i < k; i++) {
				max += (e[i] = scan.nextInt());
			}
			int cur = max;
			for (int i = 0, j = k; j < n; i++, j++) {
				if (i >= k)
					i = 0;
				cur -= e[i];
				e[i] = scan.nextInt();
				cur += e[i];
				if (cur > max)
					max = cur;
			}
			System.out.println(max);
		}

		scan.close();
		System.exit(0);
	}

}