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 Test {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		
		int length = scanner.nextInt();
		int elements = scanner.nextInt();
		
		System.out.print(1);
		for (int i = 2; i < length - elements + 1; i++) {
			System.out.print(" " + i);
		}


		int count = elements - 1;
		int current = length;
		int multiplier = -1;
		
		
		while (count >= 0) {
			System.out.print(" " + current);
			current += count * multiplier;
			multiplier *= -1;
			count--;
		}
	}
}