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 Main {
	static int n,m;
	static int[] a;
	public static void main(String[] args) throws Exception{
		Scanner cin=new Scanner(System.in);
		n=cin.nextInt(); m=cin.nextInt();
		a=new int[n+1];
		for (int i=m+2;i<=n;i++) a[i]=i;
		for (int i=m,j=1;i>=1;i-=2,j++) a[i]=j;
		for (int i=m+1,j=m+1;i>=1;i-=2,j--) a[i]=j;
		for (int i=1;i<=n;i++) System.out.print(a[i]+" ");
		cin.close();
	}
}

  		  					  			  	  	 	 	 	  	