AMC 12A 2011 Problem 19

At a competition with N players, the number of players given elite status is equal to

2^{1+\left\lfloor\log _{2}(N-1)\right\rfloor}-N

Suppose that 19 players are given elite status. What is the sum of the two smallest possible values of N ?

Note: \lfloor x\rfloor is the greatest integer less than or equal to x.

Answer Choices
A. 38
B. 90
C. 154
D. 406
E. 1024