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 Codeforces275C {
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        int l = 1, r = in.nextInt(), k = in.nextInt();
        boolean flag = true;
        while(k-- > 1){
            if(flag) System.out.print(l++ + " ");
            else System.out.print(r-- + " ");
            flag = !flag;
        }
        if (!flag) {
            while (l <= r) System.out.print(r-- + " ");
        } else {
            while (l <= r) System.out.print(l++ + " ");
        }
    }
}