AMC 12 2011a Problem 19

At a competition with $N$ players, the number of players given elite status is equal to $2^{1+\lfloor \log_{2} (N-1) \rfloor}-N$. Suppose that $19$ players are given elite status. What is the sum of the two smallest possible values of $N$?

\textbf{(A)}\ 38 \textbf{(B)}\ 90 \textbf{(C)}\ 154 \textbf{(D)}\ 406 \textbf{(E)}\ 1024