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 line[] = br.readLine().split(" ");
			int n = Integer.parseInt(line[0]);
			int k = Integer.parseInt(line[1]);
			if(n==0){break;}

			int maxi = 0;
			int sum = 0;
			int[] seq = new int[n];
			for(int i=0; i<n; i++){
				seq[i] = Integer.parseInt(br.readLine());
			}

			for(int i=0; i<k; i++){
				sum += seq[i];
			}
			maxi = sum;
			for(int i=k; i<n; i++){
				sum -= seq[i-k];
				sum += seq[i];
				maxi = Math.max(maxi, sum);
			}

			System.out.println(maxi);
		}
	}
}