Problem: Snuke has a fair N-sided die that shows the integers from 1 to N with equal probability and a fair coin. He will play the following game with them:

1. Throw the die. The current score is the result of the die.
2. As long as the score is between 1 and K-1 (inclusive), keep flipping the coin. The score is doubled each time the coin lands heads up, and the score becomes 0 if the coin lands tails up.
3. The game ends when the score becomes 0 or becomes K or above. Snuke wins if the score is K or above, and loses if the score is 0.



You are given N and K. Find the probability that Snuke wins the game.

Constraints

* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K


Output

Print the probability that Snuke wins the game. The output is considered correct when the absolute or relative error is at most 10^{-9}.

Examples

Input

3 10


Output

0.145833333333


Input

100000 5


Output

0.999973749998

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt(), k = sc.nextInt();
		
		double sum = 0;
		if(n < k) {
			sum = get(n, k);
		} else {
			sum = (n - k + 1) + get(k - 1, k);
		}
		
		sum *= (1.0 / (n * 1.0));
		System.out.println(sum);
	}
	
	public static double get(int n, int k) {
		double sum = 0;
		for(int i = 1; i <= n; i++) {
			int p = (int)Math.ceil(Math.log10((k * 1.0) / i) / Math.log10(2));
			sum += Math.pow(0.5, (p * 1.0));
		}
		return sum;
	}
}