The tower function of twos is defined recursively as follows: T(1)=2 and T(n+1)=2^{T(n)} for n \geq 1. Let A=(T(2009))^{T(2009)} and B=(T(2009))^{A}. What is the largest integer k such that
\underbrace{\log _{2} \log _{2} \log _{2} \ldots \log _{2}}_{k \text { times }} B
is defined?
Answer Choices
A. 2009
B. 2010
C. 2011
D. 2012
E. 2013