VTMO 2016 — Grade 9 — semifinal Question 1

Positive integers $a , b$ satisfy $\frac{1}{a} + \frac{2}{b} = \frac{8}{2 a + b}$ and $2010 \lt 4 a + 7 b \lt 2016$. Find $a + b$. Original choices: $A = 336 , B = 333 , C = 330 , D = 339 , E = 342$.