2021 AMC 12A Problem 12

All the roots of the polynomial z^6-10z^5+Az^4+Bz^3+Cz^2+Dz+16 are positive integers, possibly repeated. What is the value of B?

\textbf{(A) }{-}88 \qquad \textbf{(B) }{-}80 \qquad \textbf{(C) }{-}64 \qquad \textbf{(D) }{-}41\qquad \textbf{(E) }{-}40

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.