Design a HashMap data structure that supports the following operations:

• Constructor(): Initializes the hash map object with an empty map to store the key-value pairs.

• Put(key, value): Inserts a key-value pair into the hash map. If the specified key is already present in the hash map, the associated value is updated. Otherwise, the key-value pair is added to the hash map.

• Get(key): Returns the value associated with the specified key if the key exists in the hash map. Otherwise, it returns $-1$, indicating the absence of a mapping for the key.

• Remove(key): Removes the entry for the specified key from the hash map, effectively removing both the key and its associated value. This elimination only takes place when the key exists in the hash map.

Note: Your implementation should not utilize the built-in hash table libraries.

Constraints:

• $0$ $\le$ key $\le$ $10^6$
• $0$ $\le$ value $\le$ $10^6$
• At most, $10^4$ calls can be made to the Put, Get, and Remove functions.

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in hash_map.py and bucket.py in the following coding playground.