+483 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 
