Alice and Bob play the following game with two heaps of 10,000 and 20,000 marbles.
- Alice and Bob move alternatingly. Alice makes the first move.
- In every move, the active player may
(i) either remove 𝑥 ≥ 1 marbles from the first heap,
(ii) or remove 𝑦 ≥ 1 marbles from the second heap,
(iii) or remove 𝑥 ≥ 1 marbles from the first heap and 𝑦 ≥ 1 marbles from the second heap, where 𝑥 + 𝑦 is divisible by 2016.
- The player who takes the last marble wins the game.
Question: Which player is going to win this game?
(As usual, we assume that Alice and Bob both use optimal strategies.)