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 C
{

	FastScanner in;
	PrintWriter out;
	int i = 0, j = 0;


	void solve() {
		/**************START**************/
		int n = in.nextInt(), k = in.nextInt();
		if (k == 1)
		{
			for (i = 1; i <= n; i++)
			{
				out.print(i + " ");
			}
			out.println();
			return;
		}
		else if (k == 2)
		{
			out.print("1 3 2 ");
			for (i = 4; i <= n; i++)
			{
				out.print(i + " ");
			}
			out.println();
			return;
		}
		else
		{
			int lim;
			if (k % 2 == 0)
			{
				lim = k/2;
			}
			else
			{
				lim = (k+1)/2;
			}
			for (i = 1; i <= lim; i++)
			{
				out.print(i + " " + (k+2-i) + " ");
			}
			if (k % 2 == 0)
			{
				out.print((k/2 + 1) + " ");
			}
			
			for (i = k + 2; i <= n; i++)
			{
				out.print(i + " ");
			}
			out.println();

		}












		/***************END***************/
	}

	public static void main(String[] args) {
		new C().runIO();
	}

	void runIO() {
		in = new FastScanner(System.in);
		out = new PrintWriter(System.out);

		solve();

		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public FastScanner(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return null;
				st = new StringTokenizer(s);
			}
			return st.nextToken();
		}

		//This will empty out the current line (if non-empty) and return the next line down. If the next line is empty, will return the empty string.
		String nextLine() {
				st = null;
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				return s;
		}

		boolean hasMoreTokens() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return false;
				st = new StringTokenizer(s);
			}
			return true;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}