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:

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

Implement the function

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.

Public test cases

**Input**

2 2 7 8 1234 1 9999 1 1000000000000000000000 1000000000000000000000 999999999999999999999 99999999999999999999 10000000000000000000 1 1870 8428 100000 1010

**Output**

04 15 01235 10000 02000000000000000000000 1099999999999999999998 010000000000000000001 10298 0101010

**Input**

999999999999999999999999999999999999999999999999999999999999999999999999999999999 2

**Output**

1000000000000000000000000000000000000000000000000000000000000000000000000000000001

Information

- Author
- Professorat de P1
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++