You have two piles of apples: the first pile contains `a` apples and the second pile contains `b` apples. In one move you choose one pile to be the **receiving** pile and move apples into it from the other pile. The number of apples moved must be exactly the number of apples the receiving pile currently contains, so the receiving pile doubles in size. A move is legal only if the giving pile holds at least that many apples. Determine whether there is a finite sequence of moves after which both piles contain the same number of apples. Return `true` if it is possible (including when the piles are already equal), and `false` otherwise. **Function signature** ``` canBalance(a, b) -> boolean ``` **Input** - `a` — the number of apples in the first pile - `b` — the number of apples in the second pile **Output** - `true` if the two piles can be made equal through some sequence of legal moves, `false` otherwise. **Constraints** - `1 <= a, b <= 10^9` - The answer must be produced efficiently for values up to the full constraint range. **Examples** 1. `a = 3, b = 5` → `true` Move 3 apples from the second pile onto the first: `(3, 5) → (6, 2)`. Then move 2 apples from the first pile onto the second: `(6, 2) → (4, 4)`. The piles are equal. 2. `a = 1, b = 2` → `false` The reachable states cycle: `(1, 2) → (2, 1) → (1, 2) → ...` — the piles never become equal. 3. `a = 2, b = 4` → `false` `(2, 4) → (4, 2) → (2, 4) → ...` — the states repeat and equality is never reached. 4. `a = 7, b = 7` → `true` The piles are already equal; zero moves are needed.