Optimal Bid-Ask Quotes Against an Informed Trader

You are making a market in a stock whose true value $V$ is uniformly distributed on $[0, 100]$. You must quote a bid $b$ and an ask $a$, with $b < a$. The trader you face is perfectly informed: they buy from you at your ask $a$ if $V > a$, and they sell to you at your bid $b$ if $V < b$. No trade occurs when $b \leq V \leq a$. What bid and ask should you quote to maximize your expected profit? What does the optimal solution tell you about market making against a fully informed counterparty?