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;
////cf1*

public class Main {
	public static void main(String[]args){
		Scanner scanner =new Scanner(System.in);

		int n = scanner.nextInt();
		int k = scanner.nextInt();
		int[] array = new int[n];
		array[0] = 1;
		int f = 1;
		int i;
		for (i = 1; i <= k; i++) 
		{
			array[i] = array[i - 1] + f * (k - i + 1);
			f *= -1;
		}
		int current = k + 2;
		while (i < n)
		{
			array[i++] = current++;
		}

		for (int j = 0; j < n; j++)
		{
			System.out.print(array[j] + " ");  
		}

	}

}

