Implement a fully working overloaded division and modulo operators of a LargeInteger class representing numbers as a DoublyLinkedList class. Assume you have a proper DoublyLinkedList API available. Use the code of the LargeInt below. Current implementation of the division and modulo fails. Assume you have all other operators properly implemented, don't look at my current formatting as it might be bad due to me just pasting the code to fit the character limit:

class LargeInt $\{$

private:

DoublyLinkedList digits;

public:

$//$ Constructor

LargeInt$($const std::string& str $="0")\{$

for $($char c : str$)\{$

if $($std::isdigit$($c$))\{$

digits.insertBack$($c $-\text{'}0\text{'})$;

$\}$

$\}$

$\}$

LargeInt operator$/($const LargeInt& a$,$ const LargeInt& b$)\{$

if $($b $==$ LargeInt$("0"))\{$

throw std::runtime$\_$error$("$Division by zero"$)$;

$\}$

if $($a $<$ b$)\{$

return LargeInt$("0")$;

$\}$

LargeInt quotient;

LargeInt remainder;

LargeInt dividend $=$ a;

int num$\_$digits $=$ a$.$digits.size$()-$ b$.$digits.size$()+1$;

for $($int i $=0$; i $<$ num$\_$digits; $++$i$)\{$

remainder.digits.insertBack$(*$dividend$.$digits.begin$())$;

dividend.digits.deleteItem$(*$dividend$.$digits.begin$())$;

int digit $=0$;

while $($remainder $>=$ b$)\{$

remainder $=$ remainder $-$ b;

$++$digit;

$\}$

quotient.digits.insertBack$($digit$)$;

$\}$

while $(!$quotient.digits.isEmpty$()$ && $*$quotient$.$digits.begin$()==0)\{$

quotient.digits.deleteItem$(*$quotient$.$digits.begin$())$;

$\}$

if $($quotient$.$digits.isEmpty$())\{$

quotient.digits.insertBack$(0)$;

$\}$

return quotient;

$\}$

$//$ Modulo operator

LargeInt operator$\%($const LargeInt& a$,$ const LargeInt& b$)\{$

if $($b $==$ LargeInt$("0"))\{$

throw std::runtime$\_$error$("$Division by zero"$)$;

$\}$

LargeInt remainder $=$ a;

while $($remainder $>=$ b$)\{$

LargeInt temp $=$ b;

int count $=0$;

while $($remainder $>=$ temp$)\{$

temp.digits.insertBack$(0)$;

$++$count;

$\}$

temp.digits.deleteItem$($temp$.$digits.size$()-1)$;

$--$count;

remainder $=$ remainder $-$ temp;

$\}$

return remainder;

$\}$