Problem:
Score : 300 points

Problem Statement

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:

Throw the die. The current score is the result of the die.

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.

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}.

Sample Input 1

3 10

Sample Output 1

0.145833333333

If the die shows 1, Snuke needs to get four consecutive heads from four coin flips to obtain a score of 10 or above. The probability of this happening is \frac{1}{3} \times (\frac{1}{2})^4 = \frac{1}{48}.

If the die shows 2, Snuke needs to get three consecutive heads from three coin flips to obtain a score of 10 or above. The probability of this happening is \frac{1}{3} \times (\frac{1}{2})^3 = \frac{1}{24}.

If the die shows 3, Snuke needs to get two consecutive heads from two coin flips to obtain a score of 10 or above. The probability of this happening is \frac{1}{3} \times (\frac{1}{2})^2 = \frac{1}{12}.

Thus, the probability that Snuke wins is \frac{1}{48} + \frac{1}{24} + \frac{1}{12} = \frac{7}{48} \simeq 0.1458333333.

Sample Input 2

100000 5

Sample Output 2

0.999973749998

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

import org.omg.PortableServer.ID_ASSIGNMENT_POLICY_ID;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String string = sc.nextLine();
		
		String[] array = string.split(" ");
		Double[] array2 = new Double[2];
		for(int i=0; i<array.length; i++) {
				array2[i] = Double.parseDouble(array[i]);
		}
		Double[] r = new Double[]{1.0,2.0,4.0,8.0,16.0,32.0,64.0,128.0,256.0,512.0,1024.0,2048.0,4096.0,8192.0,16384.0,32768.0,65536.0};
		double ans = 0.0;
		for(int i=0; i<array2[0];i++) {
			Double a = array2[1] / (Double.parseDouble(String.valueOf(i))+1.0);
			int b = 17;
			for(int j=0; j<17; j++) {
				if(r[j] >= a) {
					b=j;
					break;
				}
			}
			ans += (1.0/array2[0])*(Math.pow(0.5,b));
		}
		System.out.println(ans);
	}

}