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;
import java.io.PrintWriter;

public class DiversePermutation {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = scan.nextInt();
		int k = scan.nextInt();
		int start = 1;
		int end = n;
		int last = 1;
		for(int i = 0; i < k; i++){
			if(i % 2 == 0){
				out.print(start+" ");
				last = start;
				start++;
			}
			else{ 
				out.print(end+" ");
				last = end;
				end--;
			}
		}
		boolean check = k % 2 == 0;
		for(int i = k; i < n; i++){
			if(check){
				last--;
			}
			else{
				last++;
			}
			out.print(last+" ");
		}
		out.flush();
		out.close();
	}
}
