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E - Geometric Progression

Score : $500$ points

Problem Statement

Given integers $A$, $X$, and $M$, find $\displaystyle \sum_{i = 0}^{X-1} A^i$, modulo $M$.

Constraints

• $1 \leq A, M \leq 10^9$
• $1 \leq X \leq 10^{12}$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$A$ $X$ $M$

Output

Print the answer.

3 4 7

5

$3^0 + 3^1 + 3^2 + 3^3 = 40$, which equals $5$ modulo $7$, so $5$ should be printed.

8 10 9

0

1000000000 1000000000000 998244353

919667211