You are given two positive integers $A$ and $M$ where $\gcd(A, M) = 1$. You have to determine whether there exists at least one integer $X$ such that $AX = 1 \pmod M$.
Okay, this is actually finding the modular multiplicative inverse exists. But here $A$ can be greater than $M$. $A$ and $M$ are $\geq 1$. So is there any case that I need to consider when $A \gt M$?