In this paper, we study the Cost-aware Target Viral Marketing (CTVM) problem, a generalization of Influence Maximization (IM). CTVM asks for the most cost-effective users to influence the most relevant users. In contrast to the vast literature, we attempt to offer exact solutions. As the problem is NP-hard, thus, exact solutions are intractable, we propose TipTop, a $(1-ε)$-optimal solution for arbitrary $ε>0$ that scales to very large networks such as Twitter. At the heart of TipTop lies an innovative technique that reduces the number of samples as much as possible. This allows us to exactly solve CTVM on a much smaller space of generated samples using Integer Programming. Furthermore, TipTop lends a tool for researchers to benchmark their solutions against the optimal one in large-scale networks, which is currently not available.