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 MyClass {
   
     public static void main(String[] args) {
     Scanner scan = new Scanner(System.in);
     int n = scan.nextInt();
     int k = scan.nextInt();
     boolean[] used = new boolean[n+1];
     int cur = 1;
        
     while(k>1)
     {
         if(!used[cur])
         {
             System.out.print(cur + " ");
             used[cur] = true;
             System.out.print((cur + k)+ " ");
             used[cur + k] = true;
             cur = cur + 1;
             k = k-2;
         }    
         else
         {
             cur = cur++;
         }
         
     }
     for(int i = cur; i <=n; i++)
     {
         if(!used[i])
             System.out.print(i + " ");
             
     }
       
   }  
}