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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/*
 public class _483C{ }
 */

public class _483C
{
	private static PrintWriter printWriter;

	public void solve() throws FileNotFoundException
	{
		InputStream inputStream = System.in;

		InputHelper inputHelper = new InputHelper(inputStream);

		PrintStream out = System.out;

		// actual solution

		int n = inputHelper.readInteger();

		int k = inputHelper.readInteger();

		int diff = n - k - 1;

		String ans = "";
		for (int i = 0, j = n; i < diff; i++, j--)
		{
			// ans += (j + " ");
			out.print(j + " ");
		}

		int an = k + 1;

		for (int i = 1, j = an; i <= j; i++, j--)
		{
			if (i == j)
			{
				// ans += (i + " ");
				out.print(i + " ");
				break;
			}
			// ans += (j + " ");
			out.print(j + " ");
			// ans += (i + " ");
			out.print(i + " ");
		}

		out.println();
		// out.println(ans.substring(0, ans.length() - 1));
		// end here

	}

	public static void main(String[] args) throws FileNotFoundException
	{
		(new _483C()).solve();
	}

	class InputHelper
	{
		StringTokenizer tokenizer = null;
		private BufferedReader bufferedReader;

		public InputHelper(InputStream inputStream)
		{
			InputStreamReader inputStreamReader = new InputStreamReader(
					inputStream);
			bufferedReader = new BufferedReader(inputStreamReader, 16384);
		}

		public String read()
		{
			while (tokenizer == null || !tokenizer.hasMoreTokens())
			{
				try
				{
					String line = bufferedReader.readLine();
					if (line == null)
					{
						return null;
					}
					tokenizer = new StringTokenizer(line);
				}
				catch (IOException e)
				{
					e.printStackTrace();
				}
			}

			return tokenizer.nextToken();
		}

		public Integer readInteger()
		{
			return Integer.parseInt(read());
		}

		public Long readLong()
		{
			return Long.parseLong(read());
		}
	}
}
