The tower function of twos is defined recursively as follows: $T(1) = 2$ and $T(n+1) = 2^{T(n)}$ for $n\geq1$. Let $A = (T(2009))^{T(2009)}$ and $B = (T(2009))^A$. What is the largest integer $k$ such that
$\underbrace{\log_{2}\log_{2}\log_{2}...\log_{2}} B$
$k$ times