F006A. Can you add up? P55982

Your task is to write a program that reads pairs of natural numbers and prints their sum.

Warning: the natural numbers that we consider in this problem can be very large (thousands of digits), you must store them in variables of |string| type. The main program is already done; do not modify it:

    int main() {
        string x, y;
        while (cin >> x >> y) cout << sum(x, y) << endl;
    }

Implement the function

    string sum(string x, string y);

that, given two strings of characters |x| and |y| that represent two natural numbers, returns a string of characters |z| that represents their sum.

To simplify the problem, suppose that neither |x| nor |y| start with ‘|0|’. Besides, suppose that |x| has, at least, the same number of digits than |y|. The number of digits of |z| must be equal to the number of digits of |z| plus one, although it causes that |z| starts with ‘|0|’.

Observations

• Remember that a string |s| with |n| characters |c| can be declared like this: |string s(n, c);|

• Remember also that the string operations like |s += ’0’;|, |s1 += s2;| or |s = s1 + s2;| are not allowed.