, 2022

The numbers $x$, $y$, $p$ and $q$ are all integers. $x$ and $y$ are variable and $p$ and $q$ are constant and positive. The four integers are related by the equation $xy = px + qy$. When $y$ takes its maximum possible value, which expression is equal to $y - x$?

(A) $pq-1$ (B) $(p-1)(q-1)$ (C) $(p+1)(q-1)$ (D) $(p-1)(q+1)$ (E) $(p+1)(q+1)$