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.io.IOException;
import java.util.Scanner;


public class C483 {

	public static void main(String[] args) throws IOException {
		Scanner in = new Scanner(System.in);
		long n = in.nextLong();
		long k = in.nextLong();
		System.out.print(1);
		long current = 1;
		long flip=1;
		for (long i=k; i>=1; i--) {
			current += flip*i;
			flip *= -1;
			System.out.print(" " + current);
		}
		for (long i = k+2; i<=n; i++){
			System.out.print(" " + i);
		}
		System.out.println();
	}
}
