Implement a size-bounded LRU cache

Design and implement an LRU (Least Recently Used) cache where the cache capacity is measured by total size, not by item count.

Each cached item has a variable size (positive integer). The cache has a maximum capacity maxSize.

Operations

Implement the following operations:

1. get(key) -> value | null
   • Return the value if key exists, else return null .
   • If the key exists, mark it as most recently used .
2. put(key, value, size)
   • Insert or update an item with the given size .
   • Mark the item as most recently used .
   • If inserting/updating causes total cached size to exceed maxSize , evict one or more least-recently-used items until totalSize <= maxSize .

Requirements / Clarifications

• size is a positive integer.
• If size > maxSize , define and document expected behavior (commonly: do not store the item at all).
• Updating an existing key may change its size; eviction may be needed.
• Target time complexity: O(1) average time for get and put (excluding time spent evicting multiple items).

Example

maxSize = 10

• put(A, ..., size=6) → total=6
• put(B, ..., size=5) → total would be 11, so evict LRU items until total<=10 (likely evict A if it is LRU)

Describe data structures and invariants you would maintain.