Hello codeforces,

Today, I am regretably in math class with the subject of modular arithmetic. While thinking about a problem, I reminded myself of a question I asked myself some time ago.

Given $$$p$$$ and $$$mod$$$, find a $$$q$$$ such that $$$q^2$$$ = $$$p$$$ (modulo $$$mod$$$). $$$mod$$$ is prime and ≫ $$$10^8$$$

Does this admit an online logarithmic-complexity solution?