  We prove, by an ad hoc method, that exact fillings with vanishing rational
first Chern class of flexibly fillable contact manifolds have unique integral
intersection forms. We appeal to the special Reeb dynamics (stronger than ADC
\`a la Lazarev) on the contact boundary, while a more systematic approach
working for general ADC manifolds is developed independently by Eliashberg,
Ganatra and Lazarev. We also discuss cases where the vanishing rational first
Chern class assumption can be removed. We derive the uniqueness of
diffeomorphism types of exact fillings of certain flexibly fillable contact
manifolds and obstructions to contact embeddings, which are not necessarily
exact.
