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
//Volume5-0516
import java.util.ArrayDeque;
import java.util.Scanner;

class Main {

    public static void main(String[] args) {

    	ArrayDeque<Integer> q = new ArrayDeque<Integer>();

        Scanner sc = new Scanner(System.in);

        while(true){

        	int n = sc.nextInt();
        	int k = sc.nextInt();

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

        	int sum = 0,
        		max;

        	q.clear();

        	int tmp;
        	for(int i=0;i<k;i++,n--){
        		q.add(tmp = sc.nextInt());
        		sum += tmp;
        	}
        	max=sum;
        	while(n-- > 0){
        		q.add(tmp = sc.nextInt());
        		sum = sum - q.poll() + tmp;
        		if(sum>max){max = sum;}
        	}
        	System.out.println(max);
        }
    }
}