HMMT 2015 A2

The fraction $\frac{1}{2015}$ has a unique "(restricted) partial fraction decomposition" of the form

$$\frac{1}{2015}=\frac{a}{5}+\frac{b}{13}+\frac{c}{31}$$

where $a, b, c$ are integers with $0 \leq a<5$ and $0 \leq b<13$. Find $a+b$.