AMC 10 2014b Problem 17

What is the greatest power of $2$ that is a factor of $10^{1002} - 4^{501}$? $\textbf{(A) } 2^{1002} \textbf{(B) } 2^{1003} \textbf{(C) } 2^{1004} \textbf{(D) } 2^{1005} \textbf{(E) }2^{1006}$