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;

/**
 * Created by lyashenko on 11.11.2014.
 */
public class Main {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int k = scan.nextInt();
        int s = n - k - 1;
        int[] seq = new int[n];
        if (k > n / 2) {
            int m = n;
            int l = s + 1;
            for (int i = 0; i < (n - s + 1) / 2; i++) {
                seq[i * 2] = m--;
                if (l != m + 1) {
                    seq[i * 2 + 1] = l++;
                }
            }
            l = 1;
            for (int i = (n - s); i < n; i++) {
                seq[i] = l++;
            }
        } else {
            for (int i = 0; i < s + 1; i++) {
                seq[i] = i + 1;
            }
            int m = n;
            int l = s + 2;
            for (int i = s + 1; i < n; i+=2) {
                seq[i] = m--;
                if ((i + 1) < n) {
                    seq[i + 1] = l++;
                }
            }
        }

        for (int i = 0; i < seq.length; i++) {
            System.out.print(seq[i] + " ");
        }
    }
}