ÖMO 1991 Problem 4

The sequence $(a_n)$ is given by $a_1=1,a_2=0$ and:

$a_{2k+1}=a_k+a_{k+1}, a_{2k+2}=2a_{k+1}$ for $k \in \mathbb{N}.$

Find $a_m$ for $m=2^{19}+91.$