Search Indexing Engine

Design a simple in-memory search indexing engine that supports three types of queries on a static collection of documents:

1. Single-word search: return the list of document IDs that contain the given word.
2. Multi-word search (AND): return the list of document IDs that contain every word in the query.
3. Sentence search: return the list of document IDs that contain the exact query string as a substring (case-insensitive).

You will implement a class SearchIndexEngine with two public methods:

• SearchIndexEngine(List<String> documents) constructs the engine from the provided documents. Each document is a string. Document IDs are the 0-based indices of the strings in the input list.
• List<Integer> search(String query, QueryType type) returns the list of document IDs that satisfy the query for the given type. The three enum values are SINGLE_WORD, MULTI_WORD, and SENTENCE. All searches are case-insensitive; both indexing and querying should treat uppercase and lowercase letters as the same.

You may assume the documents contain only ASCII printable characters and spaces. Words are sequences of non-space characters separated by one or more spaces. The order of IDs in the returned list does not matter.