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. 
//package Codeforces.Div1A_275.Code1;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/*
 * some cheeky quote
 */

public class Main
{
    FastScanner in;
    PrintWriter out;

    public void solve() throws IOException
    {
        int n = in.nextInt();
        int k = in.nextInt();

        int left = 1;
        int right = n;

        boolean isFirst = true;
        for (int i = 0; i < k; i++)
        {
            if (!isFirst)
            {
                out.print(" ");
            }
            isFirst = false;
            if (i % 2 == 0)
            {
                out.print(left++);
            } else
            {
                out.print(right--);
            }
        }

        if (k % 2 == 0)
        {
            for (int i = k; i < n; i++)
            {
                out.print(" " + right--);
            }
        } else
        {
            for (int i = k; k < n; k++)
            {
                out.print(" " + left++);
            }
        }

    }

    public void run()
    {
        try
        {
            in = new FastScanner();
            out = new PrintWriter(System.out);

            solve();

            out.close();
        } catch (IOException e)
        {
            e.printStackTrace();
        }
    }

    class FastScanner
    {
        BufferedReader br;
        StringTokenizer st;

        FastScanner()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreTokens())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }
    }

    public static void main(String[] arg)
    {
        new Main().run();
    }
}

