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 CodeForce {
    
    public static void main(String[] args) {
        Scanner in =  new Scanner(System.in);
        int n = in.nextInt() ; 
        int k = in.nextInt() ; 
        boolean plus = true ; 
        int num = 1  ;
        
        for(int i = 0 ; i < n-k - 1  ; ++i){ // 1  
               System.out.println(num++);
        }
        int factor = k ;
        for(int i =n-k - 1 ; i<n ; ++i){ // 1  ,  6
            System.out.println(num);
            if(plus){
                num+=factor ;
                plus = false ;
            }
            else{
                num-=factor ; 
                plus = true ; 
            }
            --factor ; 
        }
        
        
      
        
    }

    

}
