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 P482A {
	public static void main(String[] args) {
		Scanner keyboard = new Scanner(System.in);
		int n = keyboard.nextInt();
		int k = keyboard.nextInt();

		int[] values = { 1, n };
		int toggle = 0;
		String sep = "";
		while (n-- > 0) {
			System.out.print(sep + values[toggle]);
			values[toggle] += -(2 * toggle - 1);
			if (--k > 0) {
				toggle ^= 1;
			}
			sep = " ";
		}
		System.out.println();
	}
}
