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.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Tifuera
 */
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[] answer = new int[n];

        for (int i = 1; i <= k + 1; i++) {
            if (i % 2 == 1) {
                int m = i / 2;
                answer[k + 1 - i] = k + 1 - m;
            } else {
                answer[k + 1 - i] = i / 2;
            }
        }

        for (int i = k + 2; i <= n; i++) {
            answer[i - 1] = i;
        }

        for (int a : answer) {
            out.print(a + " ");
        }
    }

}

class InputReader {
    private BufferedReader reader;
    private String[] currentArray;
    private int curPointer;

    public InputReader(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
    }


    public int nextInt() {
        if ((currentArray == null) || (curPointer >= currentArray.length)) {
            try {
                currentArray = reader.readLine().split(" ");
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            curPointer = 0;
        }
        return Integer.parseInt(currentArray[curPointer++]);
    }

}

