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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author zodiacLeo
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        FastPrinter out = new FastPrinter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }
    
    static class TaskC
    {
        private int n;
        private int[] a;
        
        public void solve(int testNumber, FastScanner in, FastPrinter out)
        {
            n = in.nextInt();
            int k = in.nextInt();
            
            a = new int[n];
            int last = n;
            for (int i = n - k; i < n; i += 2)
            {
                a[i] = last;
                last--;
            }
            
            last = 1;
            for (int i = 0; i < n; i++)
            {
                if (a[i] == 0)
                {
                    a[i] = last;
                    last++;
                }
            }
            StringBuilder result = new StringBuilder();
            for (int i = 0; i < n; i++)
            {
                result.append(a[i] + " ");
            }
            out.println(result);
            
        }
        
    }
    
    static class FastPrinter extends PrintWriter
    {
        public FastPrinter(OutputStream out)
        {
            super(out);
        }
        
        public FastPrinter(Writer out)
        {
            super(out);
        }
        
    }
    
    static class FastScanner
    {
        public BufferedReader br;
        public StringTokenizer st;
        
        public FastScanner(InputStream is)
        {
            br = new BufferedReader(new InputStreamReader(is));
        }
        
        public FastScanner(File f)
        {
            try
            {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e)
            {
                e.printStackTrace();
            }
        }
        
        public String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                String s = null;
                try
                {
                    s = br.readLine();
                } catch (IOException e)
                {
                    e.printStackTrace();
                }
                if (s == null)
                {
                    return null;
                }
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }
        
        public int nextInt()
        {
            return Integer.parseInt(next());
        }
        
    }
}

