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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Locale;
import java.util.StringTokenizer;

public class A {

    private static final int MOD = 1000000007;

    private void solve() throws IOException {
        int n = nextInt();
        int k = nextInt();

        int l = 1;
        int r = n;
        int last = 1;
        for (int i = 0; i < k; i += 2) {
            print(l + " ");
            last = l;
            l++;
            if (i < k - 1) {
                print(r + " ");
                r--;
                last = r;
            }
        }


        if (last == l - 1) {
            for (int i = l; i <= r; i++) {
                print(i + " ");
            }
        } else {
            for (int i = r; i >= l; i--) {
                print(i + " ");
            }
        }
    }

    private String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

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

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

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

    private void print(Object o) {
        writer.print(o);
    }

    private void println(Object o) {
        writer.println(o);
    }

    private void printf(String format, Object... o) {
        writer.printf(format, o);
    }

    public static void main(String[] args) {
        long time = System.currentTimeMillis();
        Locale.setDefault(Locale.US);
        new A().run();
        System.err.printf("%.3f\n", 1e-3 * (System.currentTimeMillis() - time));
    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    private void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(13);
        }
    }
}