class Polynomial:
    def __init__(self, *argv: float):
        if len(argv) < 1:
            raise ValueError("A Polynomial has at least one coefficient.")
        if argv[-1] == 0:
            raise ValueError("The coefficient at the highest degree must not be zero.")
        self.__coefficients = tuple(argv)
        self.__order = len(argv)

    def  evaluate(self, x: float) -> tuple[float, list[float]]:
        p = self.__coefficients[-1]
        c = [p]
        for ak in self.__coefficients[-2::-1]:
            p = ak + (p * x)
            c.insert(0, p)
        return c[0], c[1:]

    def order(self):
        return self.__order

    def __add__(self, other: "Polynomial") -> "Polynomial":
        if not isinstance(other, Polynomial):
            raise ValueError("Operator + is only applicable for Polynomial.")
        coefficients = []
        if self.__order > other.__order:
            low_order = other.__order
            heigh_order = self.__order
            higher_coefficients = self.__coefficients
        else:
            low_order = self.__order
            heigh_order = other.__order
            higher_coefficients = other.__coefficients

        for i in range(0, low_order):
            coefficients.append(self.__coefficients[i] + other.__coefficients[i])
        for j in range(i+1, heigh_order):
            coefficients.append(higher_coefficients[j])
        return Polynomial(*coefficients)

    def __getitem__(self, key):
        return self.__coefficients[key]


    def __repr__(self) -> str:
        coe = []
        for c in self.__coefficients:
            coe.append(f'{c}')
        return ' '.join(coe)