Solve $19^n$ = $801777482$ $\pmod {4535332489}$ given $4535332489$ is prime.

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Solve $19^n$ = $801777482$ $\pmod {4535332489}$ given $4535332489$ is prime and without calculating any factors of $4535332488$. Is solving this possible with the current information? If so, what is $n$. Thanks for solvers.

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The answer is $n = 971428210$ which may be computed with the Baby Step Giant Step algorithm. And that doesn't require factoring $p-1$. But it can't be done by hand, since two lists of length > 60,000 must be computed.