Consider the ideal $I := (ux, uy, vx, uv)$ in the polynomial ring $\mathbb{Q}[u,v,x,y]$, where $u,v,x,y$ are indeterminates. Choose the correct statement(s) from below:\\
(A) Every prime ideal containing $I$ contains the ideal $(x,y)$;\\
(B) Every prime ideal containing $I$ contains the ideal $(x,y)$ or the ideal $(u,v)$;\\
(C) Every maximal ideal containing $I$ contains the ideal $(u,v)$;\\
(D) Every maximal ideal containing $I$ contains the ideal $(u,v,x,y)$.