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 Main{

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		int i=1;int j=n;
		int m=0;
		for(int l=1;l<=k;l++){
			if(m%2==0){
			System.out.print((i++)+" ");
			
			}
			else
				System.out.print((j--)+" ");
		
		m++;
		}
		for(int l=k;l<n;l++){
			if(m%2==0){
				System.out.print((j--)+" ");
			}
			else
				System.out.print((i++)+" ");
		}
		
	}

}