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;

public class Main {

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

		while (true) {
			String str[] = br.readLine().split(" ");
			int n = Integer.parseInt(str[0]);
			int k = Integer.parseInt(str[1]);

			if (n == 0 && k == 0)
				break;

			int a[] = new int[n];

			for (int i = 0; i < n; i++) {
				a[i] = Integer.parseInt(br.readLine());
			}
			int s[] = new int[n + 1];
			for (int i = 0; i < n; i++) {
				s[i + 1] = s[i] + a[i];
			}

			long max = Long.MIN_VALUE;
			for (int i = 0; i < n - k; i++) {
				long value = s[k + i] - s[i];
				max = Math.max(max, value);
			}
			System.out.println(max);
		}
	}
}
