Find all integer solutions to

$\displaystyle -2^0-2^1-2^2-...-2^{q-1} \equiv 0 \bmod q^{p-1}$

Where

$\displaystyle 2p \geq q $

$\displaystyle p$ is prime.

I know that the only solution is 1,1 (Using brute force through my graphing calculator)

This is actually part of another question in which I tried to solve and got stuck here. (I'm pretty sure what I've done before this is correct)

So if $\displaystyle p$ being prime is not used, it's alright.