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.Scanner;

public class Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner sc=new Scanner(System.in);
		for(;;){


			int n = sc.nextInt(),k=sc.nextInt();
			if(n+k==0)break;
			long[]a  = new long[n];
			long[]sum=new long[n+1];
			for(int i =0;i<n;i++){
				a[i]=sc.nextInt();
				sum[i+1]=sum[i]+a[i];
			}
			long max=Long.MIN_VALUE;
			for(int i=k;i<n+1;i++){
				max=Math.max(max, sum[i]-sum[i-k]);
			}
			System.out.println(max);

		}

	}
}