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 A482 {

	/**
	 * @param args
	 */
	public static void main(String[] args) {

		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		int k=scan.nextInt();
		System.out.print("1 ");
		int i=1;
		boolean flag=true;
		int max=k+2;
		while(k!=0) {
			if(flag) {
				i+=k;
			}
			else {
				i-=k;
			}
			System.out.print(i+" ");
			flag=!flag;
			k--;
		}
		for(int j=max;j<=n;j++) {
			System.out.print(j+" ");
		}
		
		scan.close();
		
	}

}
