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 BB {
public static void main(String[] args) {
	Scanner sc=new Scanner(System.in);
	int n=sc.nextInt();
	int k=sc.nextInt();
	int l = 1;
	int r;
	boolean b = true;

	r = n;
	System.out.print(r --);
	while(k > 1){
		if(b){
			System.out.print(" "+l ++);
		}
		else{
			System.out.print(" "+r --);
		}
		k --;
		b = !b;
	}
	if(b){
		while(r >= l) System.out.print(" "+r--);
	}
	else{
		while(l <= r) System.out.print(" "+l ++);
	}
	
}
 
   

}