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.io.*;
import java.util.*;
public final class diverse_perm
{
	static Scanner sc=new Scanner(System.in);
	static PrintWriter out=new PrintWriter(System.out);
	static boolean[] v;
	static int[] a;
	static int n,k;
	
	static void solve()
	{
		boolean b1=true,b2=false;
		a[1]=1;
		int i;
		v[1]=true;
		for(i=2;i<=n && k>0;i++)
		{
			if(b1)
			{
				a[i]=a[i-1]+k;
				k--;
				b1=false;
				b2=true;
				v[a[i]]=true;
			}
			else
			{
				a[i]=a[i-1]-k;
				k--;
				b1=true;
				b2=false;
				v[a[i]]=true;
			}
		}
		if(i==n+1)
		{
			for(int j=1;j<=n;j++)
			{
				out.print(a[j]+" ");
			}
			out.println("");
		}
		else
		{
			for(int j=1;j<=n;j++)
			{
				if(!v[j])
				{
					a[i]=j;
					v[j]=true;
					i++;
				}
			}
			for(int j=1;j<=n;j++)
			{
				out.print(a[j]+" ");
			}
			out.println("");
		}
	}
	
	public static void main(String args[]) throws Exception
	{
		n=sc.nextInt();
		k=sc.nextInt();
		if(k==1)
		{
			for(int i=1;i<=n;i++)
			{
				out.print(i+" ");
			}
			out.println("");
		}
		else
		{
			a=new int[n+1];
			v=new boolean[n+1];
			solve();
		}
		out.close();
	}
}