$3.$ Implement an access sharing scheme based on the cubic function y$=$x$3+7$x$2+2$ax$+5$ for a company with $5$ VPs and $8$ managers. This scheme requires one VP and two managers to grant access to a resource. Only VPs and managers are part of the scheme $($no CEO and President$).$ Every point should be used by a VP$/$manager only once $($cannot be assigned to multiple employees$).$

Show how this scheme is used to recover the coefficients for the following cases:

$4$th VP and $($a $($mod $8)+1)$th and $(($a$+1)($mod $8)+1)$th managers.