AMC 12 2014b Problem 15

When $p = \sum\limits_{k=1}^{6} k \ln{k}$, the number $e^p$ is an integer. What is the largest power of 2 that is a factor of $e^p$ ?

\textbf{(A)}\ 2^{12} \textbf{(B)}\ 2^{14} \textbf{(C)}\ 2^{16} \textbf{(D)}\ 2^{18} \textbf{(E)}\ 2^{20}