Please solve the question in great detail and explain each step. also explain how using a hash table makes it easier. Also, remmeber we have to implement our own hash as we cannot use the libraries given in Java. Here is the starter code: package A$3$;

$//$ Do NOT modify the package declaration

$//$ Do NOT add any import

$/**$

$*$ Your own implementation of a HashTable class.

$*$ Add the appropriate fields and methods you want in order to solve this problem.

$*/$

class HashTable $\{$

$//$ TODO: implement your own HashTable class

$\}$

public class A$3$Q$2\{$

$/**$

$*$ Return the number of unique integer solutions where each integer is in the range $[-50,50].$

$*$ The equation is given in the handout.

$*$ Precondition: A$,$ B$,$ C$,$ D$,$ E$,$ S are integers in the range $[-5000,5000]$

$*$ Note that the return value of this function is a long integer, not just an int.

$*$

$*$ Do NOT modify the signature of this function.

$*/$

public static long solve$($int A$,$ int B$,$ int C$,$ int D$,$ int E$,$ int S$)\{$

$//$ TODO: implement this function

return $0$;

$\}$

public static void main$($String$[]$ args$)\{$

$//$ Below are a few test cases.

$//$ Printing "true" means the return value is correct.

$//$ Each call to solve$()$ must take less than $5$ seconds.

System.out.println$(340==$ solve$(12,34,56,78,9,10))$;

System.out.println$(16665==$ solve$(20,-11,-2,0,11,-2011))$;

System.out.println$(10510100501$L $==$ solve$(0,0,0,0,0,0))$;

$\}$

$\}$