Factorial and fourth degree

For a natural number $m$ and a prime number $p$, let \deg_p(m) denote the exponent of $p$ in the canonical prime factorization of $m$.

You are given a natural number $n$ and a prime number $p$. Find the remainder of \dfrac{n!}{p^{\deg_p(n!)}} upon division by p^4.

In other words, divide $n!$ by $p$ as many times as possible, then compute the result modulo p^4.

The number $n$ is given in base $p$ notation:

where d_{L-1}, d_{L-2}, \dots, d_1, d_0 are nonnegative integers less than $p$ (the digits of $n$ in base $p$ representation).