A sequence of numbers is defined recursively by a1=1, a2=73, and
an=2an−2−an−1an−2⋅an−1for all n≥3 Then a2019 can be written as qp, where p and q are relatively prime positive inegers. What is p+q?<spanclass=′latex−bold′>(A)</span>2020<spanclass=′latex−bold′>(B)</span>4039<spanclass=′latex−bold′>(C)</span>6057<spanclass=′latex−bold′>(D)</span>6061<spanclass=′latex−bold′>(E)</span>8078