how to fix add function based on the test cases and output. BigInteger BigInteger::add$($const BigInteger& N$)$ const $\{$

$//$ Initializing variables to store the result and carry

BigInteger result;

int carry $=0$;

$//$ Creating copies of the List objects to avoid modifying the originals

List thisDigits $=$ digits;

List NDigits $=$ N$.$digits;

$//$ Initialize cursors for both BigIntegers

thisDigits.moveBack$()$; $//$ Move to the back to start from the end

NDigits.moveBack$()$;

$//$ For finding out the sign of the result

int resultSign $=$ signum;

$//$ Scroll through the digits of the two BigInteger numbers one by one

while $($thisDigits$.$position$()!=0||$ NDigits.position$()!=0||$ carry $!=0)\{$

$//$ Calculating sum of digits plus carry

int sum $=$ carry;

if $($thisDigits$.$position$()!=0)\{$

sum $+=$ thisDigits.peekPrev$()$;

thisDigits.movePrev$()$;

$\}$

if $($NDigits$.$position$()!=0)\{$

sum $+=$ NDigits.peekPrev$()$;

NDigits.movePrev$()$;

$\}$

$//$ Update the report and add the total to the result

carry $=$ sum $/$ base;

result.digits.insertAfter$($abs$($sum$)\%$ base$)$;

$\}$

$//$ Set the sign of the result

result.signum $=$ resultSign;

$//$ Changing the sign based on result

if $($resultSign $==0)\{$

result.signum $=($carry $<0)?-1$ : $1$;

$\}$ else if $($carry $<0$ && result.signum $>0)\{$

result.signum $=-$result.signum;

$\}$ else if $($carry $>0$ && result.signum $<0)\{$

result.signum $=-$result.signum;

$\}$

return result;

$\}$

These are the test cases: case Add$\_$test: $\{$

$/*$

$*$ Adding numbers fall into one of $4$ cases, denote pos $=$ positive number,

$*$ neg $=$ negative number

$*$

$*$ pos $+$ pos $=$ pos

$*$

$*$ pos $+$ neg $=0$

$*<0$

$*>0$

$*$

$*$ neg $+$ pos $=0$

$*<0$

$*>0$

$*$

$*$ neg $+$ neg $=$ neg

$*/$

A $=$ BigInteger$("+111122223333")$;

B $=$ BigInteger$("+222211110000")$;

$//$ pos $+$ pos $=$ pos

D $=$ BigInteger$("+333333333333")$;

C $=$ A $+$ B;

if $(!($C $==$ D$))$

return $1$;

$//$ add a positive and a negative integer

$//->$ pos $+$ neg $=0$

B $=$ BigInteger$("-111122223333")$;

C $=$ A $+$ B;

if $($C$.$sign$()!=0)$

return $2$;

$//->$ pos $+$ neg $>0$

B $=$ BigInteger$("-110122223333")$;

D $=$ BigInteger$("1000000000")$;

C $=$ A $+$ B;

if $($C$.$sign$()!=1)$

return $31$;

if $(!($C $==$ D$))$

return $32$;

$//->$ pos $+$ neg $<0$

B $=$ BigInteger$("-112122223333")$;

D $=$ BigInteger$("-1000000000")$;

C $=$ A $+$ B;

if $($C$.$sign$()!=-1)$

return $41$;

if $(!($C $==$ D$))$

return $42$;

$//->$ neg $+$ neg $=$ neg

A $=$ BigInteger$("-221211110000")$;

D $=$ BigInteger$("-333333333333")$;

C $=$ A $+$ B;

if $(!($C $==$ D$))$

return $5$;

return $0$;

$\}$

This is teh output: A $=91287346670000043892345634563400005619187236478$

B $=9876545439000000345634560000000002000034565430000000006543654365346534$

C $=98765454390000034563456191872363456345619187236000456456345756780000065436543$

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