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);
		int n = stdIn.nextInt();
		int k = stdIn.nextInt();
		int[] ans = new int[10];
		int index = 0;
		
		while( n != 0 || k != 0 ){
			int sum = 0;
			int[] num = new int[n];
			for(int i = 0; i < k; i++){
				num[i] = stdIn.nextInt();
				sum += num[i];
			}
			for(int i = k; i < n; i++){
				num[i] = stdIn.nextInt();
			}
		
			int max = sum;
			for(int i = 0; i < n-k; i++){
				sum = sum-num[i]+num[i+k];
				if( sum > max ){
					max = sum;
				}
				
			}
			ans[index] = max;
			index++;
			n = stdIn.nextInt();
			k = stdIn.nextInt();
		}
		for(int i = 0; i < index; i++){
			System.out.println(ans[i]);
		}
	}
}