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Binary Indexed Tree
Problem Description
Maintain prefix sums with point updates using a binary indexed tree.
Input
The functions receive the array representation, its logical size or capacity, and the operation-specific values described by their C signatures.
Output
Each operation returns or updates the represented data structure according to its interface contract.
Constraints
All indices, sizes, capacities, and stored values satisfy the bounds stated by the corresponding function contract.
Source
Classical data-structure implementation reconstructed from the verified C artifact.