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.*;
/**
 * @author panicker
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class DiversePermutation {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }
}

class Task {

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int a = in.nextInt(), b = in.nextInt();
        ArrayList<Integer> ans = new ArrayList<Integer>();
        ans.add(1);
        int i = 2, j = a, count = 0;
        boolean s = false;
        while (b > 1) {
            if (s) {
                ans.add(i);
                ++i;
            }
            if (!s) {
                ans.add(j);
                --j;
            }
            --b;
            ++count;
            s = !s;
        }

        if (count % 2 == 0) {
            for (; i <= j; ++i)
                ans.add(i);
        } else {
            for (; j >= i; --j)
                ans.add(j);
        }
        for ( i = 0; i < ans.size(); ++i)
            if (i != ans.size() - 1)
                System.out.print(ans.get(i) + " ");
            else
                System.out.print(ans.get(i));
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

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

}
