Any good way to calculate $\frac {\alpha ^ n - 1 } {\alpha - 1} \pmod{c}$ I tried by multiplying modular inverse of denominator to the numerator and then taking modulo $c$, but there are problems when the inverse does not exist. 
So is there a good way to solve this problem.
Constraints
$$ 1 \le \alpha \le 1e9 $$
$c$ is a prime
$$ 1 \le n \le 1e9 $$

Set $S_0:=1$ and then recursively $S_k:=\alpha S_{k-1}+1 \pmod c$ for all $k=1,\dotsc,n-1$. The last value $S_{n-1}$ is what you seek.
