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;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;

namespace ConsoleApp1
{
    using static Util;

    internal class Program
    {

        static void Main(string[] args)
        {
            var s = ReadIntArray();
            var n = s[0]; var k = s[1];

            var res = 0.0;
            for(var i=0; i<n; i++)
            {
                var now = k / (i + 1.0);
                var l = Math.Ceiling(Math.Log(now, 2));
                var c = Math.Pow(1 / 2.0, l);
                res += ( c/ n); ;
            }

            Console.WriteLine(res);
#if DEBUG
            Console.Read();
#endif
        }

        public static bool IsDate(string s, string format)
        {
            DateTime d = DateTime.MinValue;
            return DateTime.TryParseExact(s, format, null, System.Globalization.DateTimeStyles.None, out d);
        }
    }

    public static class Util
    {
        public static long[] ReadLongArray() => Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        public static int[] ReadIntArray() => Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        public static long ReadLong() => long.Parse(Console.ReadLine());
        public static long ReadInt() => int.Parse(Console.ReadLine());
    }
}