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 strings, return the product of num1 and num2, also represented as a string.
Note: You must not use any built-in BigInteger library or convert the inputs to integer directly.
 
Please complete the following python code precisely:
```python
class Solution:
    def multiply(self, num1: str, num2: str) -> str:
```