OBM 2021 Problem 9

Let $\alpha\geq 1$ be a real number. Define the set $$A(\alpha)=\{\lfloor \alpha\rfloor,\lfloor 2\alpha\rfloor, \lfloor 3\alpha\rfloor,\dots\}$$ Suppose that all the positive integers that does not belong to the $A(\alpha)$ are exactly the positive integers that have the same remainder $r$ in the division by $2021$ with $0\leq r<2021$ . Determine all the possible values of $\alpha$ .