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. 
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Jrusty
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		int n,m;
		Scanner in =new Scanner(System.in);
		n=in.nextInt();
		m=in.nextInt();
		int r,e;
		int[] num=new int[n];
		num[0]=1;
		int flag=0,i,j;
		for(r=1,j=0;j<n;r++,j+=2)
		{
			num[j]=r;
		}
		for(r=n,j=1;j<n;r--,j+=2)
		{
			num[j]=r;
		}
		int max=Integer.MIN_VALUE,sign=-1;
		for(r=m;r<n;r++)
		{
			if(Math.abs(num[r]-num[m-1])==1)
			{
			max=num[r];
			if(num[r]>num[m-1])
			sign=1;
			else if(num[r]<num[m-1])
			sign=0;
			}
		}
		for(r=m;r<n;r++)
		{
			num[r]=max;
			if(sign==1)
			max++;
			else if(sign==0)
			max--;
		}
		for(r=0;r<n;r++)
		{
			System.out.print(num[r]);
			if(r!=n-1)
			System.out.print(" ");
		}
	}
}