Isosceles $△ABC$ has a right angle at $C$. Point $P$ is inside $△ABC$, such that $PA=33$, $PB=31$, and $PC=8$. Legs $\overline{AC}$ and $\overline{BC}$ have length $s=\sqrt{a+b\sqrt{2}},$ where $a$ and $b$ are positive integers. What is $a+b$?