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-----
3 10

-----Sample Output-----
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 $\frac{1}{48} + \frac{1}{24} + \frac{1}{12} = \frac{7}{48} \simeq 0.1458333333$.

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