Piles Parity

Chef and Chefina are playing a game involving $N$ piles where the $i^{th}$ pile $(1\le i \le N)$ has $A_i$ stones initially. They take alternate turns with Chef starting the game. In his/her turn a player can choose any **non-empty** pile (say $i^{th}$ pile) and remove $X$ stones from it iff: - [Parity](https://en.wikipedia.org/wiki/Parity_(mathematics)) of $X$ is **same** as parity of $i$. - $