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. 
/**
 * Created with IntelliJ IDEA.
 * User: Jovfer
 * Date: 24.11.13
 * Time: 19:10
 * To change this template use File | Settings | File Templates.
 */

import java.io.*;
import java.util.StringTokenizer;

public class TaskA {
    StringTokenizer st;
    BufferedReader in;
    PrintWriter out;

    public static void main(String[] args) throws IOException {
        TaskA taskA = new TaskA();
        taskA.open();
        taskA.solve();
        taskA.close();
    }

    String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String str = in.readLine();
            if (str == null) return null;
            else st = new StringTokenizer(str);
        }
        return st.nextToken();
    }

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

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

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    private void close() {
        try {
            out.close();
            in.close();
        } catch (IOException ignore) {
        }
    }


    private void solve() throws IOException {
        int n = nextInt(), k = nextInt();
        if (n == 1) {
            for (int i = 1; i <= n; i++) {
                out.print(i + " ");
            }
            return;
        }
        while (n >= k + 1) out.print((n--) + " ");
        int down = 1, up = n;
        while (down < up) {
            out.print(down + " " + up + " ");
            down++;
            up--;
        }
        if (down == up)
            out.println(down);
    }

    private void open() {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new BufferedOutputStream(System.out));
    }
}