A sequence of numbers is defined recursively by a_{1}=1, a_{2}=\dfrac{3}{7}, and

a_{n}=\dfrac{a_{n-2} \cdot a_{n-1}}{2 a_{n-2}-a_{n-1}}

for all n \geq 3. Then a_{2019} can be written as \dfrac{p}{q}, where p and q are relatively prime positive integers. What is p+q ?

**Answer Choices**

A. 2020

B. 4039

C. 6057

D. 6061

E. 8078