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.*;
import java.io.*;
import static java.lang.Math.*;

class Main {

    public static void main( final String[] args ) {

	final Scanner stdin = new Scanner( System.in );

	while ( true ) {
	    final int n = stdin.nextInt();
	    final int k = stdin.nextInt();

	    if ( n == 0 && k == 0 ) {
		break;
	    }
	    
	    final Queue<Integer> q = new LinkedList<Integer>();
	    int maxVal = Integer.MIN_VALUE;
	    int sum = 0;
	    for ( int i = 0; i < k; i++ ) {
		final int elem = stdin.nextInt();
		q.offer( elem );
		sum += elem;
	    }
	    maxVal = max( maxVal, sum );
	    for ( int i = k; i < n; i++ ) {
		final int elem = stdin.nextInt();
		sum -= q.poll();
		sum += elem;
		q.offer( elem );
		maxVal = max( maxVal, sum );
	    }
	    System.out.println( maxVal );
	}	
    }    
}