2017 Pascal Problem 24

A town has 2017 houses. Of these 2017 houses, 1820 have a dog, 1651 have a cat, and 1182 have a turtle. If x is the largest possible number of houses that have a dog, a cat, and a turtle, and y is the smallest possible number of houses that have a dog, a cat, and a turtle, then x - y is

\textbf{(A)}\ 1182\quad \textbf{(B)}\ 638\quad \textbf{(C)}\ 563\quad \textbf{(D)}\ 619\quad \textbf{(E)}\ 466

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.