The following function calculates the factorial of a given integer.

$$ int factorial$($int x$)$

$\{$

$$ int product $=1$;

$$ while$($x $>0)$

$\{$

$$ product $*=$ x;

$$ x$--$;

$\}$

$$ return product;

$\}$

Which of the following function declarations $($prototypes$)$ is $($are$)$ valid?

$$ I.$$ int factorial$()$;

$$ II$.$ int factorial$($int$)$;

$$ III.$$ int factorial$($int x$)$;

$$IV$.$ int factorial$($int y$)$;

Group of answer choices

They are all valid

II and III only

III only

I only

II$,$ III, and IV only

III and IV oly

II and IV only