BALKAN 2022 Problem 2

Problem. Let $a, b$ and $n$ be positive integers with $a>b$ such that all of the following hold: (i) $a^{2021}$ divides $n$, (ii) $b^{2021}$ divides $n$, (iii) 2022 divides $a-b$.

Prove that there is a subset $T$ of the set of positive divisors of the number $n$ such that the sum of the elements of $T$ is divisible by 2022 but not divisible by $2022^{2}$.