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.
Input: num1 = "11", num2 = "123"
Output: "134"
Input: num1 = "456", num2 = "77"
Output: "533"
Input: num1 = "0", num2 = "0"
Output: "0"