Coin Tournament

The Thieves Guild is holding a coin tossing tournament. A total of $x$ thieves and $y$ assassins, $x + y$ participants, will take part. Initially each participant stands at a position denoted by an integer from $1$ to $x + y$. Games are played while at least two participants remain. In each game, take the participant $A$ standing at the position with the greatest number. Let that position be $k$. Participant $A$ tosses a fair coin and tries to move to position $\lfloor k / 2 \rfloor$, where some participant $B$ currently stands. If the coin comes up heads, $A$ moves to $B$'s position and $B$ is eliminated from the tournament. If it comes up tails, $A$ is eliminated and $B$ stays at the same position. The last remaining participant is the winner.

The assassins' delegation was late for registration, so the thieves took the positions from $1$ to $x$, and the assassins were left with the positions from $x + 1$ to $x + y$. The tournament treasurer wants to know in advance the probability that an assassin wins the tournament, given that every game uses a fair coin, that is, heads and tails each come up with probability $1 / 2$ and all coin tosses are independent. Find this probability.

The first line contains two integers $x$ and $y$: the number of thieves and the number of assassins ($1 \le x, y \le 1\,000\,000$).

Output the required probability as a decimal fraction. Your answer is considered correct if the absolute or relative error is less than $10^{-6}$.