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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Rubanenko
 */
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(), k = in.nextInt();
        int l = 1, r = n, last = 0;
        for (int i = 1; i <= k; i++) {
            if (i % 2 == 1) {
                out.print(l + " ");
                l++;
                last = l;
            }
            else {
                out.print(r + " ");
                r--;
                last = r;
            }
        }
        if (last == l) {
            for (int i = l; i <= r; i++) {
                out.print(i + " ");
            }
        }
        else {
            for (int i = r; i >= l; i--) {
                out.print(i + " ");
            }
        }
        out.println();
    }
}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
    }

    public String nextLine() {
        String line = null;
        try {
            line = reader.readLine();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
        return line;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(nextLine());
        return tokenizer.nextToken();
    }

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

