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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.