Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num 2 also represented as a string.

Note: You must not use any built-in library to convert the inputs to integer directly.

Write the code in C++ and take the integers num1 and num2 as input and output the product as a string.

For example:

Example 1:

Input: num1 = "2", num2 = "3" Output: "6"

Example 2:

Input: num1 = "-10", num2 = "30" Output: "-300"