300 Followers Problem.

Algebra Level 4

Over all sets of natural numbers \((k_1 , k_2 , k_3,...., k_{100})\) , how many possible values are there of

\[\large\left(\prod_{i=1}^{100}k_{i}\right)^{\left ( \sum_{i=1}^{100}k_{i} \right )} \pmod{ k_{100} } \]

This problem is original.
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