Consider the following Java code which reads a positive integer $($other than zero$)$ from user input and calculates the factorial of that number $($the factorial of an integer is the product of all integers from $1$ till the given integer$)$:

Scanner user$\_$input $=$ new Scanner$($System$.$in$)$;

int x $=$ user$\_$input.next$()$;

int i $=1$;

int factorial $=0$;

for $($i $=1$; i $<=$ x; i$++)\{$

factorial $=$ factorial $*$ i;

$\}$

println$($The factorial of $+$ x $+$ is $+$ factorial $+.)$;

a$)[6\%]$ The program is not printing the correct factorial, even for x$=1.$ Construct the backward slice $($at the point of the line of code that prints the factorial$)$ to locate the root cause for this and correct the code.

b$)[4\%]$ Calculate the dynamic slice of the original code, given an input of x$=1.$ Which one $($the static or the dynamic slice$)$ is more helpful in locating the root cause and why?