G4.3 Given two positive integers $x$ and $y, x y-(x+y)=\operatorname{HCF}(x, y)+\operatorname{LCM}(x, y)$, where $\operatorname{HCF}(x, y)$ and $\operatorname{LCM}(x, y)$ are respectively the greatest common divisor and the least common multiple of $x$ and $y$. If $c$ is the maximum possible value of $x+y$, find $c$.