def polynomial_long_division(dividend, divisor):
    # Copy the dividend so we can modify it
    dividend = dividend[:]
    result = []

    while len(dividend) >= len(divisor):
        # Degree difference
        deg_diff = len(dividend) - len(divisor)
        # Leading coefficient of the quotient term
        lead_coeff = dividend[0] / divisor[0]
        # Construct the current term of the quotient
        term = [0] * deg_diff + [lead_coeff]
        result = poly_add(result, term)

        # Subtract (divisor * term) from dividend
        subtrahend = poly_multiply(divisor, term)
        dividend = poly_subtract(dividend, subtrahend)

        # Remove leading zeroes
        while dividend and abs(dividend[0]) < 1e-10:
            dividend.pop(0)

    return result, dividend  # quotient, remainder

def poly_add(p1, p2):
    # Pad the shorter list with zeros
    diff = len(p1) - len(p2)
    if diff > 0:
        p2 = [0]*diff + p2
    elif diff < 0:
        p1 = [0]*(-diff) + p1
    return [a + b for a, b in zip(p1, p2)]

def poly_subtract(p1, p2):
    # Pad the shorter list with zeros
    diff = len(p1) - len(p2)
    if diff > 0:
        p2 = [0]*diff + p2
    elif diff < 0:
        p1 = [0]*(-diff) + p1
    return [a - b for a, b in zip(p1, p2)]

def poly_multiply(p, q):
    result = [0] * (len(p) + len(q) - 1)
    for i in range(len(p)):
        for j in range(len(q)):
            result[i + j] += p[i] * q[j]
    return result

# Example: (x^3 + 4x^2 + 18x + 17) / (x + 1)
dividend = [1, 4, 18, 17]  # x^3 + 4x^2 + 18x + 17
divisor = [1, 1]           # x + 1

quotient, remainder = polynomial_long_division(dividend, divisor)

print("Quotient:", quotient)
print("Remainder:", remainder)