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 greggy
 */
public class DiversePermutation {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        int a = 1;

        System.out.print(1 + " ");

        for (int i = 2; i <= n; i++) {
            while (k > 0) {
                if (i % 2 == 0) {
                    a = a + k;
                    System.out.print(a);
                    System.out.print(" ");
                } else {
                    a = a - k;
                    System.out.print(a);
                    System.out.print(" ");
                }
                k--;
                i++;
            }
            if (k == 0) {
                k--;
                i--;
                continue;
            }
            System.out.print(i);
            System.out.print(" ");

        }
        System.out.println();

        in.close();
    }

}