2004 Fermat Problem 22

If k is the smallest positive integer such that \left(2^k\right)\left(5^{300}\right) has 303 digits when expanded, then the sum of the digits of the expanded number is

\textbf{(A)}\ 11\quad \textbf{(B)}\ 10\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 7\quad \textbf{(E)}\ 5

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.