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.*;


public class tmp {
    public static void main(String [] args){
        Scanner scan = new Scanner(System.in);
        
        int n = scan.nextInt();
        int k = scan.nextInt();
        int min = 0, max= n+1;
        for(int i=1; i<=k; i++){
            if(i%2 == 0){
                max = (n-(i-1)/2);
                System.out.print(max + " ");
            }else{
                min = (i+1)/2;
                System.out.print(min + " ");
            }
        }
        if(k%2 == 0)
            for(int i=max-1;i>=min+1; i--)
                System.out.print(i+" ");
        else
            for(int i=min+1; i<=max-1; i++)
                System.out.print(i+" ");

        
        
        
        
        
        
        
        
        
          
        
        
        
        
        
    }
    
    
    
    
    
    
    


    
    
    
    
}
