# 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.