polynomials question pls help (really hard)

A polynomial product of the form$(1 - z)^{b_1} (1 - z^2)^{b_2} (1 - z^3)^{b_3} (1 - z^4)^{b_4} (1 - z^5)^{b_5} \dotsm (1 - z^{32})^{b_{32}},$where the $b_k$ are positive integers, has the surprising property that if we multiply it out and discard all terms involving $z$ to a power larger than 32, what is left is just $1-2z$. Determine 
$b_{32}$.
You can enter your answer using exponential notation.

Any help would be greatly appreciated