Please solve the programming task below using a self-contained code snippet in a markdown code block.

Given two non-negative integers, num1 and num2 represented as string, return the sum of num1 and num2 as a string.
You must solve the problem without using any built-in library for handling large integers (such as BigInteger). You must also not convert the inputs to integers directly.
 
Please complete the following python code precisely:
```python
class Solution:
    def addStrings(self, num1: str, num2: str) -> str:
```