from typing import Sequence
from typing import List


def poly_multiply_basic(poly1: Sequence, poly2: Sequence) -> List:
    """Multiply two univariate polynomials using direct brute-force approach."""
    # Time complexity: Theta(N^2).
    # Actually, the convolution of the vectors (a0,a1,..,an) and (b0,b1,..,bm),
    # (c0,c1,..,c(m+n)), is defined as: c[k] = sum_{i=0}^{k} (a[i]*b[k-i]).
    
    if not poly1 or not poly2:
        # If either is an empty list, return [0]
        return [0]
    
    result = [0] * (len(poly1) + len(poly2) - 1)
    for k in range(len(result)):
        for i in range(len(poly1)):
            if i <= k and i < len(poly1) and k - i < len(poly2):
                result[k] += poly1[i] * poly2[k - i]
    return result