The wait until the next event is $\mathrm{Exponential}(\text{rate})$. Return the probability it falls between a and b.

$$P(a \leq T \leq b) = e^{-\lambda a} - e^{-\lambda b}$$

Input

rate = 2.0
a = 0.5
b = 1.5

Output

0.3180923728035784