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 class HackerCup1 {
	public static void main(String[] args) throws Throwable {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		int k = Integer.parseInt(st.nextToken());
		Queue<Integer> q = new LinkedList<Integer>();
		int i = 1,j=n;
		boolean last = false;
		while(k-->0)
		{
			if(k<1)
				break;
			q.add(j--);
			if(j<n-1)
				k--;
			if(k<1)
			{
				last = true;
				break;
			}
			q.add(i++);
		}
		if(!last)
		while(i<=j)
			q.add(i++);
		else
			while(j>=i)
				q.add(j--);
		while(!q.isEmpty())
			out.append(q.poll()+" ");
		out.flush();
	}

}