Can you rewrite my program so that it doesn't use any of JAVA's built in base conversions? I$\text{'}$m not allowed to use them and I can't figure out how to do it$.$

import java.math.BigInteger;

import java.util.Scanner;

public class converter $\{$

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

Scanner scanner $=$ new Scanner$($System$.$in$)$;

System.out.println$("$Welcome to the Base Conversions Program!"$)$;

String value;

int initialBase, finalBase;

if $($args$.$length $==3)\{$

value $=$ args$[0]$;

initialBase $=$ Integer.parseInt$($args$[1])$;

finalBase $=$ Integer.parseInt$($args$[2])$;

$\}$ else $\{$

System.out.print$("$Enter the value to convert: $")$;

value $=$ scanner.next$()$;

System.out.print$("$Enter the initial base: $")$;

initialBase $=$ scanner.nextInt$()$;

System.out.print$("$Enter the final base: $")$;

finalBase $=$ scanner.nextInt$()$;

$\}$

if $($isValidInteger$($value$,$ initialBase$))\{$

String result $=$ convertInteger$($value$,$ initialBase, finalBase$)$;

System.out.println$("$Result: $"+$ result$)$;

$\}$ else $\{$

System.out.println$("$Error: Invalid input for the specified base."$)$;

$\}$

$\}$

public static boolean isValidInteger$($String theValue, int theBase$)\{$

$//$ Check if theValue is a valid expression in theBase

for $($char digit : theValue.toCharArray$())\{$

int digitValue $=$ Character.digit$($digit$,$ theBase$)$;

if $($digitValue $==-1||$ digitValue $>=$ theBase$)\{$

return false; $//$ Invalid digit for the specified base

$\}$

$\}$

return true;

$\}$

public static String convertInteger$($String theValue, int initialBase, int finalBase$)\{$

$//$ Convert theValue from initialBase to finalBase

BigInteger decimalValue $=$ convertToDecimal$($theValue$,$ initialBase$)$;

return convertFromDecimal$($decimalValue$,$ finalBase$)$;

$\}$

private static BigInteger convertToDecimal$($String value, int base$)\{$

BigInteger decimalValue $=$ BigInteger.ZERO;

BigInteger baseValue $=$ BigInteger.ONE;

for $($int i $=$ value.length$()-1$; i $>=0$; i$--)\{$

int digit $=$ Character.digit$($value$.$charAt$($i$),$ base$)$;

decimalValue $=$ decimalValue.add$($baseValue$.$multiply$($BigInteger$.$valueOf$($digit$)))$;

baseValue $=$ baseValue.multiply$($BigInteger$.$valueOf$($base$))$;

$\}$

return decimalValue;

$\}$

private static String convertFromDecimal$($BigInteger decimalValue, int base$)\{$

StringBuilder result $=$ new StringBuilder$()$;

while $($decimalValue$.$compareTo$($BigInteger$.$ZERO$)>0)\{$

BigInteger$[]$ quotientAndRemainder $=$ decimalValue.divideAndRemainder$($BigInteger$.$valueOf$($base$))$;

BigInteger quotient $=$ quotientAndRemainder$[0]$;

BigInteger remainder $=$ quotientAndRemainder$[1]$;

result.insert$(0,$ remainder.toString$($base$))$;

decimalValue $=$ quotient;

$\}$

return result.toString$()$;

$\}$

$\}$