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 a4 {

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

}
