how to modify this add function to correctly add pos and negatives, not just positives: BigInteger BigInteger::add$($const BigInteger& N$)$ const $\{$

$//$ Initialize variables to hold the result and carry

BigInteger result;

int carry $=0$;

$//$ Create 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$()$;

$//$ Determine the sign of the result

int resultSign $=$ signum;

$//$ Iterate through the digits of both BigIntegers

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

$//$ Calculate the 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$()$;

$\}$

$//$ Handle the case when the result sign chang

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

resultSign $=($sum $<0)?-1$ : $1$;

$\}$

$//$ Update carry and prepend the sum digit to the result

carry $=$ sum $/$ base;

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

$\}$

$//$ Set the sign of the result

result.signum $=$ resultSign;

return result;

$\}$