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
	 * <br>ÛèCÌvO
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scan = new Scanner(System.in);
		int max=0,sum=0,
			n,k;
		int[] list;
		while(true){
			n = scan.nextInt();		//¢
			k = scan.nextInt();
			if(n==0 && k==0){
				break;
			}
			
			list = new int[n];
			for(int i=0; i<n; i++){
				list[i] = scan.nextInt();
				if(k==i+1){			//ñÌZbg
					max = 0;
					sum = 0;
					for(int j=0; j<k; j++){
						sum += list[j];
					}
				}else if(k<=i){
					sum += list[i];
					sum -= list[i-k];
				}
				
				if(max<sum){
					max = sum;
				}
			}
			
			System.out.println(max);
		}
	}
}