IT-CESENATICO 2021 Problem 1

A positive integer $m$ is said to be $\emph{zero taker}$ if there exists a positive integer $k$ such that: $k$ is a perfect square; $m$ divides $k$ ; the decimal expression of $k$ contains at least $2021$ '0' digits, but the last digit of $k$ is not equal to $0$ .

Find all positive integers that are zero takers.