300 Followers Problem.

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.