AMC 10 2021a Problem 14

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