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.*;
import java.util.*;

public class Diverse_Permutation {
    public static void main(String args[]) {
         MyScanner sc = new MyScanner();
         out = new PrintWriter(new BufferedOutputStream(System.out));
         int n = sc.nextInt();
         int k = sc.nextInt();
         int[] a = new int[n];
         boolean[] used = new boolean[n+1];
         for(int i=0;i<n+1;i++) used[i]=false;
         used[0]=true;
         int seed=1;
         for(int i=0;i<n;i+=2){
             a[i]=seed;
             seed++;
        }
         seed = n ;
         for(int i=1;i<n;i+=2){
             a[i]=seed;
             seed--; 
         }
         
         for(int i=0;i<k;i++) {
             out.print(a[i] + " ");
             used[a[i]]=true;
             seed=a[i];      
         }
         
        
         for(int i=0;i<n-k;i++){
            // out.print("tejas\n");
             if(!used[seed-1]) {
                 out.print(seed-1 + " ");
                 used[seed-1]=true;
                 seed=seed-1;
             } else if(!used[seed+1]){
                 out.print(seed+1 + " ");
                 used[seed+1]=true;
                 seed=seed+1;
             }
         }
         
         
         out.close();
    }
      //-----------PrintWriter for faster output---------------------------------
       public static PrintWriter out;
          
       //-----------MyScanner class for faster input----------
       public static class MyScanner {
          BufferedReader br;
          StringTokenizer st;
     
          public MyScanner() {
             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;
          }

       }
       //--------------------------------------------------------
    }