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 DiversePermutation {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int largest = n;
		int smallest = 1;
		boolean altr = true;
		StringBuffer ans = new StringBuffer();
		for (int i = 0; i < k ; i++) {
			if (altr)
				ans.append((largest--) + " ");
			else
				ans.append((smallest++) + " ");
			altr = !altr;
		}
		if (altr) {
			for (int i = smallest; i <= largest; i++) {
				ans.append(i + " ");
			}
		} else {
			for (int i = largest; i >= smallest; i--) {
				ans.append(i + " ");
			}
		}
		System.out.println(ans);
	}
}
