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 DiversePermutation482A {

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

		int[] arr = new int[n];
		arr[0] = 1;
		int c = 1;
		for (int i = 0; i < n; i++) {
			arr[i] = i + 1;
		}

		int s = 0, i = 0;
		int[] a2;
		if (k > 1) {
			a2 = new int[n];
			for (; k > i; --k) {
				a2[s++] = arr[i++];
				a2[s++] = arr[k];
				arr[k] = -1;
			}
			for (; i < n; ++i) {
				if (arr[i] != -1) {
					a2[s++] = arr[i];
				}
			}
		} else {
			a2 = arr;
		}
		
		for (int j = 0; j < n; j++) {
			System.out.print(a2[j]);
			System.out.print(' ');
		}
	}

}
