NP-completeness of Bipartite Exact Cut

\textsc{Max-Cut} is a well-known NP-complete problem in which, given a graph $G$ and an integer $k$, one needs to determine whether there exists a cut of size at least $k$ in $G$. An exact version is likewise asking whether $G$ has a cut of size exactly $k$. Denote this problem by \textsc{Exact-Cut}.In this paper, we will present a reduction for \textsc{Bipartite-Exact-Cut}. The paper will be divided into two sections. The first section will assume the $NP$-completeness of \textsc{Exact-Cut} in general graphs. This proof is only meant to demonstrate a simple idea that the general case can be easily transformed to the bipartite case. We will not prove the $NP$-completeness for the general case separately. Instead, the second section will directly prove the $NP$-completeness for the bipartite case. Thus, the hardness of general case follows.