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 c483 {
    public static void main(String[]args)
    {
        Scanner sc = new Scanner(System.in);
        
        int n,k;
        n = sc.nextInt();
        k = sc.nextInt();
        
        System.out.print("1 ");
        int ult = 1;
        for(int i=2;i<=n;++i)
        {
            if(k>0)
            {
                if(i%2==0) ult = ult+k;
                else ult = ult-k;
                k--;
            }
            else ult = i;
            System.out.print(ult+" ");
        }
        System.out.println();
    }
}
