  For a small cover Q^n and any principal (Z_2)^m-bundle M^n over Q^n, it was
shown in a previous work of the author that the total sum of Z_2-Betti numbers
of M^n is at least 2^m. In this paper, we prove that when M^n is connected, the
total sum of Z_2-Betti numbers of such an M^n exactly equals 2^m if and only if
M^n is homeomorphic to a product of spheres, and Q^n in this case must be a
generalized real Bott manifold (or equivalent, Q^n is a small cover over a
product of simplices).
