Quiz: Beauty of Numbers

Sriram asked:

Imagine there is a queue of people for getting a ticket for a movie or somehing. Where should be standing in the queue to last until the manager or some guy keeps removing people at odd indices. For instance, if the queue has 5 people given a token A to E, first we remove the first set of odd numbered positions in the queue, so A, C and E are gone. Now B and D remain. Again we remove the odd numbered positions. This time B alone is gone, and D is the winner. So in a queue like that, what is the lucky position you should hold so that you survive the wave of removals?

I could give you the solution right here in front of your eyes. But that would not give you time to think to solve it on your own. So solve it and\or read the solution here.