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;

/**
 * Created by Egor on 24/10/14.
 */
public class TaskC {

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);
        String[] input = reader.readLine().split(" ");

        int n = Integer.parseInt(input[0]);
        int k = Integer.parseInt(input[1]);

        StringBuilder builder = new StringBuilder();
        if (k != 1) {
            int lastNumber = n;
            int prevNumber = 0;
            for (int i = 0; i < k; i++) {
                prevNumber = lastNumber;
                if (i % 2 == 0) {
                    lastNumber = i / 2 + 1;
                } else {
                    lastNumber = n - (i - 1) / 2;
                }
                builder.append(lastNumber).append(" ");
            }

            int startIndex = lastNumber;
            int endIndex = prevNumber;


            if ((double) startIndex == (double) n / 2.0) {
                builder.append(startIndex + 1);
            } else {
                if ((double) startIndex < (double) n / 2.0) {
                    startIndex++;
                    endIndex--;
                } else {
                    startIndex--;
                    endIndex++;
                }

                if (startIndex < endIndex) {
                    for (int i = startIndex; i <= endIndex; i++) {
                        builder.append(i).append(" ");
                    }
                } else {
                    for (int i = startIndex; i >= endIndex; i--) {
                        builder.append(i).append(" ");
                    }
                }
            }
        } else {
            for (int i = 0; i < n; i++) {
                builder.append(i + 1).append(" ");
            }
        }
        writer.println(builder.toString());
        writer.close();
    }

}
