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 {

	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);
		while(true){
			int n = stdIn.nextInt();
			int k = stdIn.nextInt();
			if((n|k)==0){
				return;
			}
			int[] a = new int[n];
			for(int i=0;i<n;i++){
				a[i] = stdIn.nextInt();
			}
			int max = 0;
			
			for(int i=0;i<k;i++){
				max += a[i];
			}
			int s = max;
			for(int i=k;i<n;i++){
				s += a[i];
				s -= a[i-k];
//			TLE -------------------------
//			for(int i=0;i<=n-k;i++){
//				int s = 0;
//				for(int j=i;j<i+k;j++){
//					s+=a[j];
//				}
				max = Math.max(max, s);
			}
			System.out.println(max);
		}
	}
}