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

public class a
{
	public static void main(String[] arg) throws IOException
	{
		new a();
	}
	public a() throws IOException
	{
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt(); int k = in.nextInt();
		ArrayDeque<Integer> q = new ArrayDeque<Integer>();
		for(int i = 1; i <= n; i++) q.add(i);
		boolean flag = true;
		while(k > 1)
		{
			if(flag) out.print(q.poll()+ " ");
			else out.print(q.pollLast() + " ");
			flag = !flag;
			k--;
		}
		while(q.size() > 0)
		{
			if(flag) out.print(q.poll() + " ");
			else out.print(q.pollLast() + " ");
		}
		in.close(); out.close();
	}

	class FastScanner 
	{
		BufferedReader reader;
		StringTokenizer tokenizer;
		public FastScanner(InputStream input)
		{
			reader = new BufferedReader(new InputStreamReader(input));
			tokenizer = new StringTokenizer("");
		}
		String next() throws IOException
		{
			while(!tokenizer.hasMoreTokens()){tokenizer = new StringTokenizer(reader.readLine());}
			return tokenizer.nextToken();
		}
		char nextChar() throws IOException{return next().charAt(0);}
		int nextInt() throws IOException{return Integer.parseInt(next());}
		double nextDouble() throws IOException{return Double.parseDouble(next());}
		long nextLong() throws IOException{return Long.parseLong(next());}
		void close() throws IOException{reader.close();}
	}
}