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: Wrong Answer)

using System.Collections.Generic;
using System;
using static System.Console;

namespace atcoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var NK = Input.ar;
            int N = NK[0];
            int K = NK[1];
            int max = Math.Min(N+1, K);
            double ans = 0.0;
            for(int i = 1; i< N; i++)
            {
                ans += Math.Pow(0.5, num(i, K));
            }
                        ans /= N;

            System.Console.WriteLine(ans);

        }
      public static int num (int index , int K)
        {
            int i = 0;
            while( index < K)
            {
                i++;
                index *= 2;

            }


            return i;


        }

        public class Input
        {

            public static string read => ReadLine();
            public static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
            public static int num => Convert.ToInt32(read);
            public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
            public static long numL => Convert.ToInt64(read);
            public const string Alfa = "abcdefghijklmnopqrstuvwxyz";
            public const int MOD = 1000000007;
        }
    }
}