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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class C {
	public static void main(String args[]) throws NumberFormatException,
			IOException {

		Stdin in = new Stdin();
		PrintWriter out = new PrintWriter(System.out);
		int n = in.readInt();
		int k = in.readInt();
		if (k % 2 == 0) {
			k /= 2;
			for(int i=n;i>n-k;i--){
				if(i==n)
					out.print(i+" "+(n-i+1));
				else
					out.print(" "+i+" "+(n-i+1));
			}
		} else {
			k /= 2;
			for(int i=n;i>n-k;i--){
				if(i==n)
					out.print((n-i+1)+" "+i);
				else
					out.print(" "+(n-i+1)+" "+i);
			}
		}
		for (int i =k+1; i <= n-k; i++) {
			if (i > 1)
				out.print(" ");
			out.print(i);
		}

		out.flush();
		out.close();

	}

	private static class Stdin {
		InputStreamReader read;
		BufferedReader br;

		StringTokenizer st = new StringTokenizer("");

		private Stdin() {
			read = new InputStreamReader(System.in);
			br = new BufferedReader(read);

		}

		private String readNext() throws IOException {

			while (!st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		private int readInt() throws IOException, NumberFormatException {

			return Integer.parseInt(readNext());

		}

		private long readLong() throws IOException, NumberFormatException {

			return Long.parseLong(readNext());

		}
	}
}
