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.*;

public class _482A_Diverse_Permutation {
    public static void main(String[] args) {
	Scanner in = new Scanner(System.in);
	int n = in.nextInt();
	int k = in.nextInt();
	int l = 1;
	System.out.print(1 + " ");
	for (int i = 0; i < k; i++)
	    System.out.print((l += i % 2 == 0 ? k - i : -(k - i)) + " ");
	for (int i = k + 2; i <= n; i++)
	    System.out.print(i + " ");
    }
}