Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.

Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.

Input

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).

Output

Print n integers forming the permutation. If there are multiple answers, print any of them.

Examples

Input

3 2


Output

1 3 2


Input

3 1


Output

1 2 3


Input

5 2


Output

1 3 2 4 5

Note

By |x| we denote the absolute value of number x. 
import java.util.*;

public class helloWorld 
{
	public static void main(String[] args) 
	{		
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int m = in.nextInt();
		
		StringBuilder ans = new StringBuilder();
		int left = n-m+1, right = n;
		for(int i = 1; i <= n; i++)
			if(i + m <= n)
				ans.append(i + " ");
			else
				if( (i-n+m) % 2 == 1)
					ans.append(right-- + " ");
				else
					ans.append(left++ + " ");
					
		
		System.out.println(ans);

		in.close();
	}
}