Congruences of the colorful grid

How can I build a colorful grid in Mathematica representing the rest of $$x ^ {y}$$ modulo a given prime number $$p$$? (with coordinates)
As such:

nt.number theory – Number of solutions to certain quadratic congruences

assume $$p$$ and $$q$$ are prime numbers and $$p neq q$$ and $$| x |, | y | so how many solutions can we expect from congruences
$$x ^ 2y ^ 2-ry ^ 2 equiv a bmod p$$
$$x ^ 2y ^ 2-r ^ x 2 equiv b bmod q$$ or $$r, r, a, b in mathbb Z backslash {0 }$$ are given with $$mathsf {GCD} (ab, pq) = 1$$?