output_description: Print the probability that Snuke wins the game. The output is considered
  correct when the absolute or relative error is at most 10^{-9}.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N K
attempt: n, k = map(int, input().split())
  a = n
  n0 = n
  i = 0
  sum = 0
  power_list = [0] * 24
  if n > k:
      power_list[0] = n - k + 1
      n = k - 1
      a = k
  i = 1
  a = k
  while a != 1:
      if a % 2 == 0 and a // 2 > n:
          a = a // 2
          k = a
          i += 1
      elif a % 2 == 0 and a // 2 <= n:
          power_list[i] = n - a // 2 + 1
          n = a // 2 - 1
          a = a // 2
          i += 1
      else:
          a += 1
  for i in range(24):
      sum += (1 / 2) ** i * power_list[i]
  # print(power_list)
  print(sum / n0)
  
problem_description: 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:
  
    1. Throw the die. The current score is the result of the die.
    2. 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.
    3. 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.
samples: [{"input": "3 10", "output": "0.145833333333\n    \n\n  * 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}.\n  * 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}.\n  * 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}.\n\nThus, the probability that Snuke wins is \\frac{1}{48} + \\frac{1}{24} +\n\\frac{1}{12} = \\frac{7}{48} \\simeq 0.1458333333.\n\n* * *"}, {"input": "100000 5", "output": "0.999973749998"}]