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 A482 {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);

		int n = scan.nextInt();
		int k = scan.nextInt();
		
		int pos = k - 1;
		
		StringBuffer ans = new StringBuffer();
		
		for (int i = n - 1; i >= 0; i--) {
		    if (i > pos) {
		        ans.append((i + 1) + " ");
		    }
		    else {
		        int dif = pos - i;
		        
		        if (dif % 2 == 0) {
		            ans.append((dif / 2 + 1) + " ");
		        }
		        else {
		            dif--;
		            ans.append((pos + 1 - dif / 2) + " ");
		        }
		    }
		}
		
		System.out.print(ans);
	}
}