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.*;
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
import java.math.*;
public class Main 
{ 
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader()
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next()
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine();
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
   public static void main(String args[])
    {
        FastReader sc=new FastReader();
        PrintWriter pw=new PrintWriter(System.out);
        int t=1;//sc.nextInt();
        while(t-->0)
        {
          int n=sc.nextInt(),k=sc.nextInt(),dup=k;
          int a[]=new int[n];
          for(int i=0;i<n;i++)
          a[i]=i+1;
          StringBuffer sb=new StringBuffer();
          sb.append(1+" ");Integer p=1;a[0]=0;
          for(int i=1;i<=k;i++)
          {
              if(i%2!=0)
              {
              p+=(dup--);    
              sb.append(p+" ");
              a[p-1]=0;
              }
              else {p-=(dup--);sb.append(p+" ");a[p-1]=0;}
          }
          for(int w:a) 
          if(w!=0) sb.append(w+" ");
          pw.println(sb);
        }
        pw.close();
    }
}
  