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;

/**
 * Created by yuu on 15/4/17.
 */
public class Problem482A {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();

        int prev = 1;
        boolean plus = true;
        System.out.print(prev + " " );
        for (int i = k; i > 0; i--) {
            if (plus) {
                prev += i;
            }
            else {
                prev -= i;
            }
            System.out.print(prev + " ");
            plus = !plus;
        }
        for (int i = k + 2; i <= n; i++) {
            System.out.print(i + " ");
        }
        System.out.println();
    }
}
