Find constants when Vectors are parallel

Question

I apologize for the "title".

Q: The points A, B and C have position vectors OA = a, OB = b and OC = m(2a+b). Find m if BC is parallel to OA.

ANS: 1

I've tried the following:

BC = OC - OB
BC = m(2a+b) - b
And;
m(2a+b) - b = k(a)

Answer 1

hint

$$BC=m(2a+b)-b=$$ $$=2ma+(m-1)b$$

What happens if $m=1$.