City Transit Route Optimizer

You have been tasked with optimizing a transit route for a city's public transportation system.

In this problem, you are given a directed graph where each node represents a transit stop and each edge represents a direct connection between stops with an associated travel time (a positive integer). Additionally, you are given:

• A starting stop (source).
• A destination stop (target).
• A maximum allowed number of transfers (i.e., you cannot use more than a given number of edges).

Your task is to design and implement an algorithm that finds the fastest route from the source to the target while using no more than the allowed number of transfers. If no such route exists, your solution should indicate that as well.

Please ensure your solution handles large graphs efficiently, considers edge cases, and is written using clear modular code. You may assume that the graph is provided as an adjacency list or any other reasonable representation of your choice.

Good luck!