Triangle $ABC$ has $AC=3$, $BC=4$, and $AB=5$. Point $D$ is on $\overline{AB}$, and $\overline{CD}$ bisects the right angle. The inscribed circles of $\triangle ADC$ and $\triangle BCD$ have radii $r_a$ and $r_b$, respectively. The value of \frac{r_a}{r_b} is given in the form \frac{k}{m}(n-\sqrt{p}). Please calculate the value of k+m+n+p.

Let's think step by step and output the final answer within \boxed{}.
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