from collections import defaultdict

class Polynomial(object):
	__slots__ = ["koefficients"]

	def __init__(self, koefficients):
		self.koefficients = list(koefficients)
		# Remove trailing zeros.
		while(self.koefficients and self.koefficients[-1] == 0):
			self.koefficients.pop()

	def __call__(self, x):
		if(not isinstance(x, (float, int, complex))):
			raise TypeError("unsupported type for {}: {}".format(x, type(x)))

		result = 0
		for i, a in enumerate(self.koefficients):
			result += a * x**i

		return result

	def __add__(self, other):
		if(not isinstance(other, Polynomial)):
			raise TypeError("cannot add {} and {}".format(type(self), type(other)))

		p1 = self.koefficients
		p2 = other.koefficients
		if(len(other.koefficients) > len(self.koefficients)):
			p1, p2 = p2, p1

		p2 += [0] * (len(p1) - len(p2))

		return Polynomial([a + b for a,b in zip(p1, p2)])

	def __mul__(self, other):
		if(isinstance(other, (int, float, complex))):
			return Polynomial([a * other for a in self.koefficients])

		if(not isinstance(other, Polynomial)):
			raise TypeError("cannot add {} and {}".format(type(self), type(other)))

		result = defaultdict(int)
		for i, k1 in enumerate(self.koefficients):
			for j, k2 in enumerate(other.koefficients):
				result[i + j] += k1 * k2

		
		return Polynomial(result[i] for i in range(max(result)))

	def __repr__(self):
		return "{}({})".format(type(self).__name__, self.koefficients)
	def __str__(self):
		return " + ".join(["{}*x**{}".format(a, i) for i, a in enumerate(self.koefficients)])