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.Scanner;

public class Permutations {
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int n = in.nextInt();
    int k = in.nextInt();
    for (int i = 1; i < n - k; i++) {
      System.out.print(i + " ");
    }
    int s = n - k;
    int sign = 1;
    int c = k;
    for (int i = n - k; i <= n; i++) {
      System.out.print(s + " ");
      s = s + c * sign;
      c--;
      sign *= -1;
    }
    System.out.println();
  }
}
