Let $x$ and $y$ be integers satisfying $41x + 53y = 12$. Find the residue of $x$ modulo 53. (Express your answer as an integer from 0 to 52.

$$\small{\text{ Let $x$ and $y$ be integers satisfying $41x + 53y = 12$. Find the residue of $x$ modulo 53. }}\\ \small{\text{ (Express your answer as an integer from 0 to 52.) }}$$

$$\small{\text{ If $x=264$ and $y=-204$ then $41x + 53y = 12$. }}\\ \small{\text{ The residue of $x\pmod{ 53 } = 52$. }}$$