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 static AtCoderer.Exter;
using static System.Console;
using static System.Math;
using System.Linq;

namespace AtCoderer
{

    public class App
    {
        public static void Main(string[] args)
        {
            double Perc = 0;
            var r = readarr;
            double n = r[0], k = r[1];
            for(int i = 1;i<=n;i++)
            {
                Perc += Pow(0.5,Ceiling(Log(k/i, 2))) / n;
            }
            cout = Perc;
            Console.ReadKey();
        }
    }
    public static class Exter
    {
        public static void rep(int loop, Action<int> act)
        {
            for (int i = 0; i < loop; i++)
                act(i);
        }
        public static int ToInt(this string v) => int.Parse(v);
        public static int Max(params int[] p) => p.Max();
        public static long Max(params long[] p) => p.Max();
        public static int Min(params int[] p) => p.Min();
        public static long Min(params long[] p) => p.Min();
        public static int Gcd(int a, int b) => a > b ? GcdRecursive(a, b) : GcdRecursive(b, a);
        private static int GcdRecursive(int a, int b) => b == 0 ? a : GcdRecursive(b, a % b);
        public static object cout
        {
            set
            {
                Console.Write(value.ToString());
                Console.WriteLine();

            }
        }
        public static void ToCout<t>(this IEnumerable<t> v)
        {
            cout = string.Join(",", v);
        }
        public static int[] readarr
        {
            get
            {
                preadarr = Console.ReadLine().Split().Select(s => int.Parse(s)).ToArray();
                return preadarr;
            }
        }
        public static int[] preadarr;
    }
}