Binomials and Powers (noch nicht übersetzt)

Problem 830

Let $\displaystyle S(n)=\sum\limits_{k=0}^{n}\binom{n}{k}k^n$.

You are given, $S(10)=142469423360$.

Find $S(10^{18})$. Submit your answer modulo $83^3 89^3 97^3$.