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: Runtime Error)

package com.company;
import java.util.*;
public class Main {
    public static void main(String[] args) {

task3();

    }

    public static void task1(){
    	Scanner s = new Scanner(System.in);
	    int n = s.nextInt(), m = s.nextInt() - 1;
	    char[] cs = s.next().toCharArray();
	    //A - a = -32
	    cs[m] += ('a' - 'A');
	    System.out.println(cs);
	}

	public static void task2(){
		Scanner s = new Scanner((System.in));
		int n = s.nextInt();
		int fh = n / 100;
		int sh = n % 100;
		System.out.println(isMonth(fh) ? (isMonth(sh) ? "AMBIGUOUS " : "MMYY") : (isMonth(sh) ? "YYMM" : "NA"));
	}

    public static Boolean isMonth(int i){
    	return (1 <= i) && (i <= 12);
	}

	public static void task3(){
    	Scanner s = new Scanner(System.in);
    	int n = s.nextInt(), k = s.nextInt();
		double ans = 0;
		for (int i = 1; i <= n; i ++){
			double tmp = i;
			while (tmp < k){
				tmp *= 2;
			}
			ans += (1/(tmp/(i * 1.0))) * (1/ (1.0 * n));
		}

		System.out.println(ans);

	}




}