Nuro's onboard software may receive numeric values that exceed the range of native integer types. Given two signed decimal integers as strings, return their exact product as a normalized decimal string.
Do not convert either input to a native integer or use a library routine that performs the entire multiplication. Implement the grade-school multiplication algorithm using digit operations.
Implement multiply_strings(a, b), where a and b are strings matching the format [+-]?\d+. Return a string containing the product with no unnecessary leading zeroes, except that zero must be returned as "0". A leading plus sign is not included in the output.
def multiply_strings(a, b):