If $$$p$$$ and $$$r$$$ are relatively prime you use Euler's theorem $$$p^{\phi(r)} = 1$$$ mod $$$r$$$. So you need to calculate $$$q!$$$ mod $$$\phi(r)$$$. $$$\phi$$$ is the Euler totient function, for a prime $$$r$$$ it is just $$$r-1$$$. You can find the answer even if $$$(p, r) > 1$$$, but it involves additional steps.