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;
class Program
    {
        static void Main(string[] args)
        {
            //とりあえず数値を読み込む
            string[] input = Console.ReadLine().Split(' ');
            int n = int.Parse(input[0]);
            int k = int.Parse(input[1]);


            //得点に対して確率を出す
            double sum = 0;

            for (int i = 1; i <= n; i++)
            {
                double purpose = (double)k/(double)i;
                if (purpose > 1.0)
                {
                    int j = 0;
                    //出さないとならない表の数を求める
                    while (purpose >= Math.Pow(2, j))
                        j++;
                    //確率を出す
                    double temp = Math.Pow(0.5, j) / (double)n;
                    //確率を足す
                    sum += temp;
                }
                else
                    sum += 1.0 / (double)n; //1倍以下であれば1/2の確率で勝てる

            }
          
            //結果を示す
            Console.WriteLine(sum);
        }
    }