This question evaluates competence in designing an efficient, stateful ledger API and associated data structures, emphasizing correctness under invalid inputs, performance at scale, integer overflow handling, unit testing for edge cases, and transactional (atomic batch) behavior.

Design and implement a banking ledger for n accounts labeled 1..n with initial balances. Provide an API: deposit(id, amount) -> bool, withdraw(id, amount) -> bool, transfer(fromId, toId, amount) -> bool. Rules: return false for invalid account IDs or insufficient funds; otherwise apply updates and return true. Constraints: up to 200,000 operations, amounts up to 10^12, target O(