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.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.Map.Entry;
import java.util.function.Function;
import java.util.function.Supplier;

public class tests {
	static Scanner in = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

	public static void main(String[] test) throws NumberFormatException, IOException {
		int n = in.nextInt();
		int k = in.nextInt();
		int l = 1;
		int r = n;
		for (int i = 1; i < k; i++) {
			if (i % 2 == 0) {
				out.print(r + " ");
				r = r - 1;
			} else {
				out.print(l + " ");
				l = l + 1;
			}
		}
		if (k % 2 == 0) {
			for (int i = k; i <= n; i++) {
				out.print(r + " ");
				r = r - 1;
			}
		} else {
			for (int i = k; i <= n; i++) {
				out.print(l + " ");
				l = l + 1;
			}
		}

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

	/*
	 * static class Scanner { BufferedReader br; StringTokenizer st;
	 * 
	 * Scanner() { br = new BufferedReader(new InputStreamReader(System.in)); }
	 * 
	 * Scanner(String file) throws FileNotFoundException { br = new
	 * BufferedReader(new FileReader(file)); }
	 * 
	 * String next() throws IOException { while (st == null ||
	 * !st.hasMoreTokens()) st = new StringTokenizer(br.readLine()); return
	 * st.nextToken(); }
	 * 
	 * int nextInt() throws NumberFormatException, IOException { return
	 * Integer.parseInt(next()); }
	 * 
	 * String nextLine() throws IOException { return br.readLine(); }
	 * 
	 * long nextLong() throws NumberFormatException, IOException { return
	 * Long.parseLong(next()); }
	 * 
	 * }
	 */
}
