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.*;
import java.math.*;
import java.io.PrintStream;
import static java.lang.Math.*;

public class Task275C {

    public static Scanner in = new Scanner(System.in);
    public static PrintStream out = System.out;

    public static void main(String[] args) {
        int n = in.nextInt();
        int k = in.nextInt();

        int prev = 1;
        int curr = prev;

        while (prev <= n) {
            k = min(k, n - prev);
            int sign = 1;
            for (int i = k; i >= 0; i--) {
                out.print(curr + " ");
                curr += i * sign;
                sign *= -1;
            }
            prev += k + 1;
            curr = prev;
        }
    }

}