Find the maximum integer $m$ such that $m! \cdot 2022!$ is a factorial of an integer.
Problem
Source: 44th International Tournament of Towns, Senior O-Level P1, Fall 2022
Tags: number theory, factorial, Tournament of Towns
Source: 44th International Tournament of Towns, Senior O-Level P1, Fall 2022
Tags: number theory, factorial, Tournament of Towns
Find the maximum integer $m$ such that $m! \cdot 2022!$ is a factorial of an integer.