12. If \(\displaystyle \log_2x \) and \(\displaystyle \log_2y\) are distinct positive integers,

\(\displaystyle \quad\;\;\;\)and \(\displaystyle \log_x2 + \log_y2 \,=\,\tfrac{1}{2}\), find \(\displaystyle xy.\)

\(\displaystyle \qquad\quad (A)\;64\qquad (B)\;128 \qquad (C)\;256 \qquad (D)\;512\qquad (E)\;1024\)