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.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.*;

public class Main implements Runnable
{
	private class Edge {

		public int to;
		public int cost;
		private int from;

		public Edge(int from, int to, int cost) {
			this.from=from;
			this.to=to;
			this.cost=cost;
		}


	}
	public static void main(String args[])
	{
		new Main().run();
	}
	public void run()
	{
		try {
			solve();
		} catch (IOException e) {
			e.printStackTrace();
		}
		out.flush();
	}
	
	private void solve() throws IOException
	{
		int n,k;
		n=in.nextInt();
		k=in.nextInt();
		ArrayList<Integer> res=new ArrayList<Integer>();
		int pv=1;
		int turn=1;
		res.add(1);
		for(int i=k;i>0;i--)
		{
			pv=pv+i*turn;
			turn=-1*turn;
			res.add(pv);
		}
		int val=1+k;
		while(val<n)
			res.add(++val);
		for(int i:res)
		{
			out.print(i);
			out.print(" ");
		}
		out.println();
	}


	class Scanner
	{
		BufferedReader in;
		StringTokenizer token;
		String delim;
		Scanner(Reader reader)
		{
			in=new BufferedReader(reader);
			token=new StringTokenizer("");
			this.delim=" \n";
		}
		Scanner(Reader reader, String delimeters)
		{
			in=new BufferedReader(reader);
			token=new StringTokenizer("");
			this.delim=delimeters;
		}
		public boolean hasNext() throws IOException
		{
			while(!token.hasMoreTokens())
			{
				String line=in.readLine();
				if(line==null) return false;
				token=new StringTokenizer(line,delim);
			}
			return true;
		}
		String next() throws IOException
		{
			return hasNext()?token.nextToken():null;
		}
		int nextInt() throws IOException
		{
			return Integer.parseInt(next());
		}
		long nextLong() throws IOException
		{
			return Long.parseLong(next());
		}
		double nextDouble() throws IOException 
		{
			return Double.parseDouble(next());
		}
		int[] nextInts(int n) throws IOException
		{
			int[] res=new int[n];
			for(int i=0;i<n;i++)
				res[i]=nextInt();
			return res;
		}
	}
	private Scanner in=new Scanner(new InputStreamReader(System.in),"\n\r\t ");
	private PrintWriter out=new PrintWriter(new BufferedWriter(
			new OutputStreamWriter(System.out)));
}