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.util.Scanner;

public class divperm {  
  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
    int numints = scan.nextInt();
    boolean[] avail = new boolean[numints];
    int kunique = scan.nextInt();
    
    for (int i = 0; i < numints; ++i)
      avail[i] = false;
    
    int left = 0, r = numints - 1;
    
    for (int i = 0; i < kunique; ++i) {
      avail[(i & 1) == 0 ? left : r] = true;
      
      if ((i & 1) == 0) {
        System.out.print((1 + (left++)));
      }
      
      else {
        System.out.print((1 + (r--)));
      }
      
      System.out.print(' ');
    }
    
    if ((kunique & 1) == 1) {
      
    	for (int i = 0; i < numints; ++i) {
    	  if (!avail[i]) {
    		  System.out.print(i + 1);
    		  System.out.print(' ');
    	  }
    	}
    	
    } else {
    	
    	for (int i = numints - 1; i >= 0; --i) {
    	  if (!avail[i]) {
        	System.out.print(i + 1);
        	System.out.print(' ');
    	  }
    	}     
    	
    }
  }
}
