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.ArrayDeque;
import java.util.Deque;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		while (in.hasNext()) {
			final int n = in.nextInt();
			final int k = in.nextInt();
			if (n == 0 && k == 0) {
				System.exit(0);
			}
			int max = Integer.MIN_VALUE, val = 0;
			Deque<Integer> deq = new ArrayDeque<Integer>(k);
			for (int i = 0; i < n && in.hasNext(); i++) {
				final int number = in.nextInt();
				if (i < k) {
					val += number;
					max = val;
				} else {
					final int f = deq.pollFirst();
					val += (number - f);
					if (val > max) {
						max = val;
					}
				}
				deq.offerLast(number);

			}
			System.out.println(max);
		}

	}
}