One Stone or Two Stones

Chef and Chefina are playing a game. There are two piles numbered $1$ and $2$. Pile $1$ contains $X$ stones while Pile $2$ contains $Y$ stones. Chef starts the game. - In his turn, Chef can either remove $1$ stone each from both the piles **or** remove $2$ stones from pile $1$. - On the other hand, Chefina, in her turn, can either remove $1$ stone each from both the piles **or** remove $2$ ston