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;

/**
 * Maximum Sum
 */
public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = "";

		int n, k, sum = 0, max1 = 0, max2 = 0;
		int[] list;

		while (!(line = br.readLine()).equals("0 0")) {
			n = Integer.parseInt(line.substring(0, line.indexOf(' ')));
			k = Integer.parseInt(line.substring(line.indexOf(' ') + 1));
			list = new int[n];
			for (int i = 0; i < n; i++) {
				list[i] = Integer.parseInt(br.readLine());
			}
			max1 = 0;
			for (int i = 0; i < k; i++) {
				max1 += list[i];
			}
			sum = max1;
			for (int i = k; i < n; i++) {
				sum = sum - list[i - k] + list[i];
				if (sum > max1)
					max1 = sum;
			}
			System.out.println(max1);
		}
	}
}