The sequence \left\{a_{n}\right\} is defined by
$$ a_{0}=1, a_{1}=1 \text {, and } a_{n}=a_{n-1}+\frac{a_{n-1}^{2}}{a_{n-2}} \text { for } n \geq 2 \text {. }
$$ The sequence \left\{b_{n}\right\} is defined by
$$ b_{0}=1, b_{1}=3, \text { and } b_{n}=b_{n-1}+\frac{b_{n-1}^{2}}{b_{n-2}} \text { for } n \geq 2
$$Find \frac{b_{32}}{a_{32}}.