Recall how the Fast Fourier Transform (FFT) can be used to multiply two polynomials efficiently by converting the problem into point-value representation, performing point-wise multiplication, and then converting back to coefficient form.

Consider how to represent large integers as polynomials where each coefficient corresponds to a digit (or a group of digits) of the number, and how the multiplication of these polynomials relates to the multiplication of the original integers.

Implement the FFT-based multiplication by first padding the polynomials with zeros to make their lengths a power of two, then applying the Cooley-Tukey algorithm to compute the FFT, perform point-wise multiplication, and finally use the inverse FFT to obtain the result polynomial, which can be converted back to the product of the original integers.