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.ArrayList;
import java.util.Scanner;


public class ProbA {
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int x = 1;
        int cc = 0;
        int h = k;
        do
        {
            cc++;
            System.out.print("" + x + " ");
            x += k;
            if(k < 0) k = -(k + 1);
            else k = -(k - 1);
        }while(cc < h + 1);
        for(int i = h + 2; i <= n; i++)
            System.out.print("" + i + " ");
    }
}
