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 eai_jovi_ta_afim_de_uns_elementos_diferenciados {
    
    public static void main(String[] args){
    
        Scanner sc = new Scanner(System.in);
        
        int n = sc.nextInt();
        int k = sc.nextInt();
        sc.nextLine();
        
        int min = 1;
        
        if(k%2 == 0){
            System.out.print(n);
            n--;
        }else{
            System.out.print(min);
            min++;
        }
        k--;
        
        while (k>0){
            if(k%2 == 0){
                System.out.print(" "+n);
                n--;
            }else{
                System.out.print(" "+min);
                min++;
            }
            k--;
        }
        
        for (int i = min; i<= n; i++)
            System.out.print(" "+i);
        
    }
    
}

				  		 		  	 	 		 	 	  	   		