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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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[] res = new int[n];
        int left = 1;
        int right = n;
        boolean ok = true;
        for (int i = 0; i < k; ++i) {
            if (ok) { res[i] = right; --right; }
            else { res[i] = left; ++left; }
            ok ^= true;
        }
        if (k % 2 == 0) {
            for (int i = k; i < n; ++i) {
                res[i] = left;
                ++left;
            }
        } else {
            for (int i = k; i < n; ++i) {
                res[i] = right;
                --right;
            }
        }

        for (int x : res)
            out.print(x + " ");
        out.println();
    }
}

class InputReader {
    BufferedReader in;
    StringTokenizer st;

    public InputReader(InputStream stream) {
        in = new BufferedReader(new InputStreamReader(stream));
        eat("");
    }

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

    public String next() {
        while (!st.hasMoreTokens())
            eat(nextLine());
        return st.nextToken();
    }

    public String nextLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            throw new InputMismatchException();
        }
    }

    public void eat(String str) {
        if (str == null) throw new InputMismatchException();
        st = new StringTokenizer(str);
    }
}

