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.math.*;
import java.util.*;


public class Main {


	public static class pair implements Comparable<pair>
	{
		int a;
		int b;
		public pair(int pa, int pb)
		{
			a = pa; b= pb;
		}
		@Override
		public int compareTo(pair o) {
			if(this.a < o.a)
				return -1;
			if(this.a > o.a)
				return 1;
			return Integer.compare(o.b, this.b);
		}
	}


	//int n = Integer.parseInt(in.readLine());
	//int n = Integer.parseInt(spl[0]);
	//String[] spl = in.readLine().split(" ");
		
	public static void main (String[] args) throws Exception
	{	
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] spl = in.readLine().split(" ");
		int n = Integer.parseInt(spl[0]);
		int k = Integer.parseInt(spl[1]);
		StringBuffer sb = new StringBuffer();
		for (int i = 1; i <= n-1-k; i++) {
			sb.append(i);
			sb.append(" ");
		}
		for (int i = 1; i <=k+1; i++) {
			if(i%2==1)
			{
				sb.append((i+1)/2+(n-1-k));
				sb.append(" ");
			}
			else
			{
				sb.append(n - (i/2-1));
				sb.append(" ");
			}
		}
		System.out.println(sb.toString().trim());
	}

}