IKMC 2022 - Grades 11-12 - Set 2 - Self-study Question 28

A sequence satisfies $0<a_1<1$ and, for every $n\ge1$, $a_{2n}=a_2a_n+1$, $a_{2n+1}=a_2a_n-2$. Given $a_7=2$, find $a_2$.