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 ProC {
	static int n,k;
	static int[] aa=new int[100005];

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