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.InputStream;
import java.io.OutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.BufferedReader;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
	public void solve(int testNumber, InputReader in, PrintWriter out) {
		int n = in.nextInt();
		int k = in.nextInt();
		int a = 1;
		int b = k + 2;
		boolean plus = true;
		out.print("1 ");
		while (k > 0) {
			if (plus) {
				a = a + k;
				out.print(a);
				out.print(" ");
			} else {
				a = a - k;
				out.print(a);
				out.print(" ");
			}
			k--;
			plus = !plus;
		}
		for (int i = b; i <= n; i++) {
			out.print(i);
		    out.print(" ");
		}
		out.println();
	}
}

class InputReader {
	public BufferedReader reader;
	public StringTokenizer tokenizer;
	
	public InputReader(InputStream stream) {
		reader = new BufferedReader(new InputStreamReader(stream), 32768);
		tokenizer = null;
	}
	
	public String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}
	
	public int nextInt() {
		return Integer.parseInt(next());
	}
}