Score : $600$ points
Among the sequences of length $K$ consisting of integers, $A=(A_1, \ldots, A_K)$, how many satisfy all of the conditions below?
Find the count modulo $998244353$.
$0\leq A_i \leq M-1$ for every $i(1\leq i\leq K)$.
$\displaystyle\prod_{i=1}^{K} A_i \equiv N \pmod M$.
Input is given from Standard Input in the following format:
$K$ $N$ $M$
Print the answer.
2 3 6
5
The five sequences $A$ satisfying the conditions are $(1,3),(3,1),(3,3),(3,5),(5,3)$.
10 0 2
1023
1000000000 20220326 1000000000000
561382653
Be sure to find the count modulo $998244353$.