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 C483 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        int z = n - k;
        int temp = 1;
        StringBuilder str = new StringBuilder();
        str.append(1);
        int left = 2;
        int right = n;
        int m = n - k - 1;
        for (int i = 0; i < m; ++i) {
            str.append(" ");
            str.append(left++);

        }

        while (left <= right) {
            str.append(" ");
            str.append(right--);
            if (left <= right) {
                str.append(" ");
                str.append(left++);
            }
        }
        System.out.println(str);
    }
}
