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.*;
import java.lang.*;

public class c {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n  = in.nextInt();
		int k = in.nextInt();
		int t = n;
		int s = -1;
		for (int i = 0; i < k; i++){
			out.print(t);
			out.write(' ');
			t += (n - 1 - i) * s;
			s = -s;
		}
		t += (n - 1 - (k - 1)) * s;
		for (int i = k; i < n; i++){
			t = t - s;
			out.print(t);
			out.write(' ');
		}
		in.close();
		out.close();
	}
}