Best stopping card for an ace-placement prize

Alice chooses a number $k$ from $1$ to $52$, then turns over the top $k$ cards of a well-shuffled standard deck. She wins if the $k$th card she turns is an ace and exactly one ace remains among the $52-k$ unturned cards. Which $k$ maximises her chance of winning?

$k=35$. Winning needs two aces among the first $k-1$ cards, an ace at position $k$, and one ace in the rest, so the probability is proportional to $(k-1)(k-2)(52-k)$. The continuous maximiser is about $35.2$; comparing integers, $k=35$ gives $19074$ versus $19040$ at $k=36$.