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

import static java.lang.Math.*;

public class CodeforcesA implements Runnable {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int n) throws IOException {
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = readInt();
        return array;
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    public static void main(String[] args) {
        new Thread(null, new CodeforcesA(), "", 128 * (1L << 20)).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    void debug(Object... objects) {
        if (DEBUG) {
            for (Object o : objects) {
                System.err.println(o.toString());
            }
        }
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            time();
            memory();
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    boolean DEBUG = false;

    void solve() throws IOException {

        int n = readInt();
        int k = readInt();

        for (int i = 0; i < n-k; i++)
            out.print((n - i) + " ");
        int a = 1;
        int b = k;
        for (int i = 0; i < k; i++) {
            if (i % 2 == 0)
                out.print(a++ + " ");
            else
                out.print(b-- + " ");
        }

    }
}