Incremental Game

Alice and Bob found two piles of stones: one with $X$ stones, and the other with $Y$ stones. They decide to play a game using these piles. Alice and Bob are always trying to one-up each other, so they decide to play under the following rules: - The players take turns moving, with Alice going first. - On Alice's first move, she must choose one of the piles, and remove **at least** $1$ and **at