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.math.BigInteger;
import java.util.Scanner;
import java.io.PrintWriter;
 
public class Main {  
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
    
    int n = in.nextInt();
    int k = in.nextInt();
    
    Boolean[] used = new Boolean[n];
    for (int i = 0; i < n; ++i)
      used[i] = false;
    
    int l = 0, r = n - 1;
    
    for (int i = 0; i < k; ++i) {
      used[(i & 1) == 0 ? l : r] = true;
      if ((i & 1) == 0)
        out.print((1 + (l++)));
      else
        out.print((1 + (r--)));
      out.print(' ');
    }
    
    if ((k & 1) == 1) {
      for (int i = 0; i < n; ++i) {
        if (!used[i]) {
          out.print(i + 1);
          out.print(' ');
        }
      }
    } else {
      for (int i = n - 1; i >= 0; --i) {
        if (!used[i]) {
          out.print(i + 1);
          out.print(' ');
        }
      }      
    }
      
    out.close();
  }
}