Need help with this C++ project.

A singly-linked list can be used to store large integers one digit at a time. For example, the integer 1234 could be stored in a list by storing 1 in the first node, 2 in the second node, 3 in the third node, and 4 in the last node. However, for this assignment you may find it more useful to store the digits backwards; that is, store 4 in the first node, 3 in the second node, 2 in the third node, and 1 in the last node. You will see why this is the case shortly. Write a program in C++ that reads two positive integers that are of arbitrary length and then outputs the sum of the two numbers. Your program will read the digits as values of type char so that the number 1234 is read as the four characters '1', '2', '3', and '4'. As the characters are read they are changed to values of type int and stored in a list. (Now you can see the first reason why storing the digits backwards has an advantage.) After the first number has been read your program reads the second number, storing it in a second list. Your program will perform the addition by implementing the usual paper-and-pencil addition algorithm. (Now you should discover the second reason why storing the digits backwards is advantageous.) The result of the addition is stored in a list and the result is then written to the screen. Include a loop that allows the user to continue to do more additions until the user says the program should end. Of course, your multiple precision addition code should be formulated as a function that accepts a pair of lists, returning a list as its result (the sum of the two inputs). You might want to base your List class on a simplification of the Node class described in our textbook.

It did not provide any linked list class for this assignment. We suppose to write program for what it stated above in bold.