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.Arrays;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;
import static java.lang.Character.toLowerCase;


public class Main {

    // input
    static int n;
    static int k;
    
    /**
     * input
     */
    static void input(){
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        k = sc.nextInt();
        sc.close();
    }
 
    /**
     * solver
     */
    static void solve(){
        double ans = 0;
        int cMax = 0;

        for (int i =1;i<=n;i++) {
            int c = 0;  // # of coin toss requred. p = (1/2)^n
            int j = i;
            while (j < k) {
                j *= 2;
                c ++;
            }
            if (i == 1) cMax = c;
            ans += Math.pow(2, cMax - c);
        }

        ans *= 1.0 / n / Math.pow(2, cMax);

        System.out.println(ans);
    }

    public static void main(String args[]) {

        input();

        solve();
    }
}