import itertools


class Poly:

    def __init__(self, elements):
        self.elements = {}

        i = len(elements) - 1
        for e in reversed(elements):
            self.elements[f"x{i}"] = e
            i -= 1

    def __str__(self):
        return str(self.elements)

    def __mul__(self, other):
        elements = {}

        for e in self.elements:
            for f in other.elements:
                coefficient = self.elements[e] * other.elements[f]
                degree = f"x{int(e[1:])+int(f[1:])}"

                if elements.get(f"{degree}") is None:
                    elements[degree] = coefficient
                else:
                    elements[degree] += coefficient

        return Poly(list(reversed(list(elements.values()))))

    def __mod__(self, other):
        elements = {}

class PolyIntField:

    def __init__(self, int_modulo, poly_modulo):
        self.int_modulo = int_modulo
        self.poly_modulo = Poly(poly_modulo)
        self.elements = list(itertools.product([x for x in range(0, int_modulo)]
                                               , repeat=len(poly_modulo) - 1))

    def get_nilpotents(self):
        nilpotents = []

        # for element in self.elements:



if __name__ == "__main__":
    # a = PolyIntField(3, [1, 1, 2, 2])
    # print(a.elements)
    # print(len(a.elements))
    b = Poly([4, 8, 1, 3])
    c = Poly([1, 4])

    print(b.elements)
    print(b * c * c)
    # c = Poly()