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 Round275_C_Diverse_Permutation {

	public static void main(String[] args) {
		Scanner x = new Scanner(System.in);
		int n = x.nextInt(), k = x.nextInt() ,temp = 1, tempk = k + 1;
		int[] set = new int[k + 2];
		
		for (int i = 1; i <= k + 1; i += 2) {
			set[i] = temp;
			temp++;
		}

		for (int i = 2; i <= k + 1; i += 2) {
			set[i] = tempk;
			tempk--;
		}
		for (int i = 1; i <= k + 1; i++) {
			System.out.print(set[i] + " ");
		}
		for (int i = k + 2; i <= n; i++) {
			System.out.print(i + " ");
		}

	}
}
