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.*;

class Main{
	public static void main(String[] args){
		Solve s = new Solve();
		s.solve();
	}	
}

class Solve{
	Solve(){}
	
	Scanner in = new Scanner(System.in);

	void solve(){
		while(in.hasNext()){
			int n = in.nextInt(), k = in.nextInt();
			if(n == 0 && k == 0) return;
			int[] a = new int[n];
			for(int i = 0; i < n; i++) a[i] = in.nextInt();
			int ans = 0 , t;
			for(int i = 0; i < k; i++){
				ans += a[i];
			}
			t = ans;
			int s = 0;
			for(int i = k; i < n; i++){
				t = t + a[i] - a[s];
				s++;
				ans = Math.max(ans,t);
			}
			System.out.println(ans);
		}
	}
	
	
}