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.PrintStream;
import java.util.Scanner;

/**
 * @author Roman Elizarov
 */
public class Round_275_A {
	public static void main(String[] args) {
		new Round_275_A().go();
	}

	int n;
	int k;

	void go() {
		// read input
		Scanner in = new Scanner(System.in);
		n = in.nextInt();
		k = in.nextInt();

		// solve
		int[] result = solve();

		// write result
		PrintStream out = System.out;
		for (int i = 0; i < result.length; i++) {
			if (i > 0)
				out.print(' ');
			out.print(result[i]);
		}
		out.println();
	}

	int[] solve() {
		int[] a = new int[n];
		a[0] = 1;
		int lo = 2;
		int hi = n;
		int last = 1;
		int dir = 1;
		for (int i = 1; i < k; i++) {
			if (i % 2 == 1) {
				last = hi--;
				dir = -1;
			} else {
				last = lo++;
				dir = 1;
			}
			a[i] = last;
		}
		for (int i = k; i < n; i++) {
			last += dir;
			a[i] = last;
		}
		return a;
	}
}
