You begin with start units. Each round you win one unit with probability p and lose one otherwise, stopping at either goal or 0. Return the probability of reaching goal first.

With $q = 1 - p$ and $r = q/p$:

$$P = \begin{cases} \dfrac{\text{start}}{\text{goal}} & p = 0.5 \\[6pt] \dfrac{1 - r^{\text{start}}}{1 - r^{\text{goal}}} & p \neq 0.5 \end{cases}$$

Input

start = 10
goal = 20
p = 0.5

Output

0.5