Custom Priority Queue

Your task is to design and implement a custom priority queue with the following operations:

1. insert(value, priority): Insert a new element with the specified unique value and its associated priority.
2. peek(): Return (but do not remove) the element with the highest priority.
3. extract_max(): Remove and return the element with the highest priority.
4. change_priority(value, new_priority): Update the priority of an existing element identified by its unique value to a new priority.

Requirements:

• The priority queue must always be able to return or remove the element with the highest priority efficiently.
• Aim to achieve logarithmic time complexity (O(log n)) for each of the operations listed above.
• You may choose any programming language for your implementation.
• Write tests to demonstrate that your priority queue behaves as expected.

Focus on designing the underlying data structures to support quick access for all operations. Provide inline comments in your code to explain your implementation choices.