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.InputStream;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.StringTokenizer;

/*07:05:45PM

 String x =sc.next();
 char inp [] = x.toCharArray();
 SimpleDateFormat displayFormat = new SimpleDateFormat("HH:mm");
 SimpleDateFormat parseFormat = new SimpleDateFormat("hh:mm a");
 Date date = parseFormat.parse(x.substring(0, 5)+" "+x.substring(8, 10));
 System.out.println(displayFormat.format(date)+":"+x.substring(6, 8));
 */

public class Main {
	

	public static void main(String[] args) throws Exception
	{
		Scanner sc = new Scanner(System.in);
		int n =sc.nextInt() , k =sc.nextInt();k--;
		int i =1;
		int nxt = n-(k+1);k++;
		boolean even = true;
		if(k%2==1 && k!=1)
		{

			if(k!=1){
			while(k-->0)
			{
				if  (even){
					System.out.print((n-(i)+1)+" ");
					even =false;
				}
				else{
					System.out.print((i++)+" ");
					even = true;
				}
				
			}
			}
			else nxt = n;
			while(nxt-->0)
				System.out.print((n-(++i)+1)+" ");
		}
		else {
		if(k!=1){
		while(k-->0)
		{
			if  (even){
				System.out.print((n-(i)+1)+" ");
				even =false;
			}
			else{
				System.out.print((i++)+" ");
				even = true;
			}
			
		}
		}
		else nxt = n;
		while(nxt-->0)
			System.out.print((i++)+" ");
		}
	}
}

class Pair {
	public int x, y;

	Pair(int a, int b) {
		x = a;
		y = b;
	}
}
class Triple implements Comparable<Triple>{
	public int x, y,z;

	Triple(int a, int b, int c) {
		x = a;
		y = b;
		z=c;
	}

	@Override
	public int compareTo(Triple o) {
		// TODO Auto-generated method stub
		return (o.x==x && o.y ==y && o.z==z)?0:-1;
	}
	
}

class Scanner {
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream s) {
		br = new BufferedReader(new InputStreamReader(s));
	}

	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

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

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

	public String nextLine() throws IOException {
		return br.readLine();
	}

	public double nextDouble() throws IOException {
		String x = next();
		StringBuilder sb = new StringBuilder("0");
		double res = 0, f = 1;
		boolean dec = false, neg = false;
		int start = 0;
		if (x.charAt(0) == '-') {
			neg = true;
			start++;
		}
		for (int i = start; i < x.length(); i++)
			if (x.charAt(i) == '.') {
				res = Long.parseLong(sb.toString());
				sb = new StringBuilder("0");
				dec = true;
			} else {
				sb.append(x.charAt(i));
				if (dec)
					f *= 10;
			}
		res += Long.parseLong(sb.toString()) / f;
		return res * (neg ? -1 : 1);
	}

	public boolean ready() throws IOException {
		return br.ready();
	}

}
