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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;


public class Main {

    static class FastScanner{
        BufferedReader s;
        StringTokenizer st;
        
        public FastScanner(){
            st = new StringTokenizer("");
            s = new BufferedReader(new InputStreamReader(System.in));
        }
        
        public FastScanner(File f) throws FileNotFoundException{
            st = new StringTokenizer("");
            s = new BufferedReader (new FileReader(f));
        }
        
        public int nextInt() throws IOException{
            if(st.hasMoreTokens())
                return Integer.parseInt(st.nextToken());
            else{
                st = new StringTokenizer(s.readLine());
                return nextInt();
            }
        }
        
      public double nextDouble() throws IOException{
            if(st.hasMoreTokens())
                return Double.parseDouble(st.nextToken());
            else{
                st = new StringTokenizer(s.readLine());
                return nextDouble();
            }
        }
      
        public long nextLong() throws IOException{
            if(st.hasMoreTokens())
                return Long.parseLong(st.nextToken());
            else{
                st = new StringTokenizer(s.readLine());
                return nextLong();
            }
        }
        
        public String nextString() throws IOException{
            if(st.hasMoreTokens())
                return st.nextToken();
            else{
                st = new StringTokenizer(s.readLine());
                return nextString();
            }
            
        }
        public String readLine() throws IOException{
            return s.readLine();
        }
        
        public void close() throws IOException{
            s.close();
        }
        
    }
      private static FastScanner s = new FastScanner();   
      private static PrintWriter ww = new PrintWriter(new OutputStreamWriter(System.out));
     
      static int count=0;
     public static void main(String[] args) throws IOException 
     {
        
         int n =s.nextInt();
         int k=s.nextInt();
         int a[] = new int[n];
         int count=0;boolean arc = true;int i=1;
           if(k!=1)
           {                  while(arc)
                           {
                                 
                               a[count]=i;ww.print(" "+a[count]);count++;i++;
                               a[count]=n;ww.print(" "+a[count]);count++;n--;
                               k=k-2;//ww.println(" ... "+a[count-1]+"  "+a[count-2]+"  "+k+" count "+count);
                               if(k==0)
                               {
                                   arc=false;
                                   if(i+1!=n)
                                   for(int t=n;t>=i;t--)
                                   ww.print(" "+t);
                                   else
                                    for(int h=n;h>=i;h--)   
                                    ww.print("  "+(h));
                               }
                               else if(k==1)
                               {
                                   arc=false;
                                   for(int t=i;t<=n;t++)
                                    ww.print(" "+t);
                               }
                              
                           }  
              }  
              else
           {
               for(int m=1;m<=n;m++)
                ww.print(" "+m);
           }
  
         s.close();
         ww.close();
     }
     public static int gcd(int a, int b){
        return b == 0 ? a : gcd(b,a%b);
    }
    

}
/*zabardast swappimng of sorting
/*
    for(int h=0;h<n;h++)
        {  int temp,temp1,temp2;
             for(int y=h+1;y<n;y++)
           {
             if(a[y][2]>=a[h][2])
             {
              
             temp=a[y][2];                 //////sorting
             a[y][2]=a[h][2]; 
              a[h][2]=temp;
              temp1=a[y][0];
              a[y][0]=a[h][0];
              a[h][0]=temp1;
              temp2=a[y][1];
              a[y][1]=a[h][1];
              a[h][1]=temp2;
           
             }
           }  
        }
*/