P4720 [Template] Extended Lucas Theorem / exLucas

This is a template problem.

Compute $${\mathrm{C}}_n^m \bmod{p}$$ where $\mathrm{C}$ is the binomial coefficient.

One line with three integers $n, m, p$, with meanings as described in the statement.

Output one integer in one line, representing the answer.

For $100\%$ of the testdata, $1 \le m \le n \le {10}^{18}$, $2 \le p \le {10}^6$, and it is **not guaranteed** that $p$ is a prime number. Translated by ChatGPT 5