TSQL Challenge 55 - Multiply two very long decimal strings and return the product

We recently saw a number of challenges that deal with Binary, Decimal and Hexadecimal strings (TSQL Challenge 40 and 51). Here is yet another challenge that deals with Decimal strings, but presents a different problem.

Your task is to multiply two positive integer strings and return their product. The strings can be really long: up to 1024 digits :-)