The domain of the function f(x)=\log _{\dfrac{1}{2}}\left(\log _{4}\left(\log _{\dfrac{1}{4}}\left(\log _{16}\left(\log _{\dfrac{1}{16}} x\right)\right)\right)\right) is an interval of length \dfrac{m}{n}, where m and n are relatively prime positive integers. What is m+n ?
Answer Choices
A. 19
B. 31
C. 271
D. 319
E. 511