Multiplying digit lists

A whole number is given as a list of its decimal digits, most significant first: [1, 3, 2, 1] is 1321. Multiply two such numbers and return the product in the same form, with no leading zeros (zero itself is [0]).

multiply([1, 3, 2, 1], [2, 2, 1, 3])   # [2, 9, 2, 3, 3, 7, 3]
multiply([9, 9], [0])                  # [0]

This problem is about writing Karatsuba’s method yourself, so work on the digits. Do not turn the lists into Python ints: Python’s own multiplication already uses Karatsuba’s method in C (lesson 5), so that would skip the exercise. The tests cannot check this; it is up to you.

Limits

• Up to 12,000 digits in each number. The schoolbook method, O(n²), is too slow for the largest test; aim for O(n¹·⁵⁸⁵).
• The inputs have no leading zeros, except the number 0 itself.