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.io.*;
import java.util.*;

public class P3 {
	public static void main (String[] args) {
		Scanner sc = new Scanner (System.in);
		PrintStream op = System.out;
		int n = sc.nextInt(), k = sc.nextInt();
		for (int i = 1; i <= n - k; i++)
			op.print(i + " ");
		int l = n - k + 1, r = n;
		boolean isR = true;
		while (l <= r) {
			if (isR) {
				op.print(r + " ");
				r--;
			}
			else {
				op.print(l + " ");
				l++;
			}
			isR = !isR;
		}
		op.println();
		sc.close();
	}
}
