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;
using System.Collections;
using System.Collections.Generic;

namespace ABC126 {
  class ProblemC {
    static void Main(string[] args) {
      int[] input = Input.nums;
      double pow = 0;
      double ans = 0;
      for (int i = 1; i <= input[0]; i++) {
        if (i >= input[1]) {
          pow = 0;
        } else {
          pow = Math.Ceiling(Math.Log((double)input[1] / i, 2));
        }
        ans += 1.0 / (input[0] * 1 << (int)pow);
      }
      System.Console.WriteLine(ans);
    }
    static int foo(int n) {
      switch (n) {
        case 1:
          return 4;
        case 2:
          return 3;
        case 3:
        case 4:
          return 2;
        case 5:
        case 6:
        case 7:
        case 8:
        case 9:
          return 1;
        default:
          return 0;
      }
    }
  }
  public class Input {
    public static string str => System.Console.ReadLine();
    public static string[] strs => str.Split(' ');
    public static char[] charArr => str.ToCharArray();
    public static int num => int.Parse(str);
    public static int[] nums => Array.ConvertAll(strs, int.Parse);
    public static long numL => long.Parse(str);
    public static long[] numLs => Array.ConvertAll(strs, long.Parse);
  }
}