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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
namespace ConsoleApplication4.Properties
{
    public class Class1
    {
        public static void Main()
        {
            var a =Console.ReadLine();
           String [] n= a.Split();
           double N =  int.Parse(n[0]);
           double K = int.Parse(n[1]);
           double sum = 0;
           double Sum = 0;
           double Sum2 = 0;
           double loglog = 0;
           for (int i = 1; i <= N; i++)
           {
               if (i<K)
               {
                   Sum = (K / i);
                   loglog = (int) Math.Log(Sum, 2);
                   if (Math.Pow(2, loglog)!=Sum)
                   {
                       loglog += 1;
                   }
                   sum += (1 / N) * (Math.Pow((0.5), loglog));
               }
               else
               {
                   sum += (1 / N);
               }

           }
           Console.WriteLine(sum);
        }
    }
}