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.

A hash map is a fundamental data structure found in various programming languages. Its key feature is facilitating fast access to a value associated with a given key. Designing an efficient hash map involves addressing two main challenges:

1. Hash function design: The hash function serves to map a key to a location in the storage space. A good hash function ensures that keys ...