HMMT 2015 Algebra #2

The fraction $\dfrac{1}{2015}$ has a unique "(restricted) partial fraction decomposition" of the form $\dfrac{1}{2015}=\dfrac{a}{5}+\dfrac{b}{13}+\dfrac{c}{31},$ whrer $a, \; b, \; c$ are integers with $0 \le a<5$ and $0 \le b < 13$. Find $a+b$.

정답 $14$