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 Main {

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

}
