Exercise $1$: Factorials, done recursively.

Create a function called factorial, defined as follows:

int factorial$($int theNum$)$;

This function should take an integer argument and return an integer result. It should work as follows:

If given a number less than zero, it should return a value of $-1,$ representing an error.

If given a $0$ or $1,$ it should return a value of $1.$

If given a number larger than $1,$ it should compute the factorial of the number minus $1,$ and

multiply it by that number. $($For example, for factorial$(6),$ it would return the product of $6$ times

factorial$(5).$ This is a direct analog to the idea of mathematical induction.

Don't use any for$()$ or while $()$ loops in your function; if done recursively, you don't need any.

It's $OK($and expected$)$ to use a for$()$ loop in main$()$ to test your function.

It is possible to do this in three lines of code $($and probably even fewer$),$ but this is not required.

Create a testbench program $-$ main$()$ and all that $-$ to test your factorial function. What is the highest

number for which it can correctly compute the factorial?

Now, replace all of your type int with type unsigned long long. $($Remember to do this for the function

parameters, as well as the individual variables. Also recall you will need $"\%$llu" for the printf$()$ format.

Does your program work differently now? Does it work for larger numbers? What is going on$?$