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 div275C
{
	BufferedReader in;
	PrintWriter ob;
	StringTokenizer st;
	public static void main(String[] args) throws IOException {
		new div275C().run();
	}
	void run() throws IOException {
		//in=new BufferedReader(new FileReader("input.txt"));
		in=new BufferedReader(new InputStreamReader(System.in));
		ob=new PrintWriter(System.out);
		solve();
		ob.flush();
	}
	void solve() throws IOException {
		int n=ni();
		int k=ni();
		boolean vis[]=new boolean[n+1];
		int start=1,j=k;
		List<Integer> list=new ArrayList<Integer>();
		for(int i=1;;i++) {
			//System.out.println(" lol "+start);
			vis[start]=true;
			list.add(start);
			if(i%2==0) {
				start=start-j;
			}
			else {
				start=start+j;
			}
			--j;
			if(j==0) {list.add(start);break;}
		}
		//System.out.println(start);
		for(int i=1;i<=n;i++) {
			if(!vis[i]) {
				int x=Math.abs(i-start);
				if(x>=1 && x<=k) 
				{
					list.add(i);
					start=i;
				}
			}
		}
		for(int i : list)
			ob.print(i+" ");
	}
	String ns() throws IOException {
		return nextToken();
	}
	long nl() throws IOException {
		return Long.parseLong(nextToken());
	}
	int ni() throws IOException {
		return Integer.parseInt(nextToken());
	}
	double nd() throws IOException {
		return Double.parseDouble(nextToken());
	} 
	String nextToken() throws IOException {
		if(st==null || !st.hasMoreTokens())
			st=new StringTokenizer(in.readLine());
		return st.nextToken();
	}
}