Binary Search and Efficiency

The Expedia app maintains a sorted list of unique property IDs for a search result page. Implement binary search to return the index of a target property ID, or -1 if the ID is not present.

Formal Specification

Implement search_property_ids(property_ids, target):

1. property_ids is a sorted list of unique integers in ascending order.
2. target is an integer property ID.
3. Return the zero-based index of target when it exists.
4. Return -1 when target is absent.

Your solution must use binary search rather than scanning every element. Explain why the search is efficient and state its time and space complexity.