For $X \sim \mathcal{N}(\mu, \sigma^2)$, return the threshold above which exactly a q fraction of the distribution lies. This is the cut-off an anomaly detector would use for a target alert rate.

You need the inverse normal CDF. There is no closed form, so bisect on the standard normal: find z with $\Phi(z) = 1 - q$, then return $\mu + z\sigma$.

Input

mu = 0.0
sigma = 1.0
q = 0.05

Output

1.6448536269514715