Model the problem as a directed graph where edges represent prerequisites, and use topological sorting to determine the order of course selection.

Use Kahn's algorithm for topological sorting, but modify it to account for the constraint of taking at most `k` courses per semester, tracking the current semester's load and available courses.

Implement a priority queue (max-heap) to always select the `k` most "independent" courses (those with the fewest remaining prerequisites) in each semester, ensuring optimal scheduling and minimizing the total semesters required.