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 mayn {
	

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