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

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