A binary operation \diamond has the properties that a \diamond(b \diamond c)=(a \diamond b) \cdot c and that a \diamond a=1 for all nonzero real numbers a, b, and c. (Here the dot \cdot represents the usual multiplication operation.) The solution to the equation 2016 \diamond(6 \diamond x)= 100 can be written as \dfrac{p}{q}, where p and q are relatively prime positive integers. What is p+q ?
Answer Choices
A. 109
B. 201
C. 301
D. 3049
E. 33,601