import sys
import ast

class Polynomial:
    
    n = 0

    def __init__(self, coeff_list):
        self.degree = len(coeff_list) - 1
        self.coefficients = [x % Polynomial.n for x in coeff_list]

    def __pow__(self, n):
        result = self
        for i in range(n):
            result = Polynomial.multiply(result, result)
        return result

    @staticmethod
    def add(p1, p2):
        result = []
        f = p1.coefficients
        g = p2.coefficients
        if len(f) >= len(g):
            result = f
            for i in range(len(g)):
                result[i] = f[i] + g[i]
        else:
            result = g
            for i in range(len(f)):
                result[i] = f[i] + g[i]
        result = [x % int(Polynomial.n) for x in result]        
        return Polynomial(result)

    @staticmethod
    def multiply(p1, p2):
        result = [0] * (p1.degree + p2.degree + 1)
        f = p1.coefficients
        g = p2.coefficients
        for i in range(len(f)):
            for j in range(len(g)):
                result[i+j] += f[i] * g[j]
        result = [x % int(Polynomial.n) for x in result]
        return Polynomial(result)

    @staticmethod
    def divide(p1, p2):          
        
        def inverse(x):
            for i in range(1, int(Polynomial.n)):
                r = (i * x) % int(Polynomial.n)
                if r == 1:
                    break
            else:
                raise ZeroDivisionError
            return i    
           
        if p1.degree < p2.degree:
            return p1
        f = p1.coefficients
        g = p2.coefficients
        g_lead_coef = g[-1]
        g_deg = p2.degree
        while len(f) >= len(g):
            f_lead_coef = f[-1]
            tmp_coef = f_lead_coef * inverse(g_lead_coef)
            tmp_exp = len(f) - 1 - g_deg
            tmp = []
            for _ in range(tmp_exp):
                tmp.append(0)
            tmp.append(tmp_coef)
            tmp_poly = Polynomial(tmp)
            sub = Polynomial.multiply(p2, tmp_poly)
            f = [x - y for x, y in zip(f, sub.coefficients)]
            f = [x % int(Polynomial.n) for x in f]
            while f and f[-1] == 0:
                f.pop()
        return Polynomial(f)

    @staticmethod
    def gcd(p1, p2):
        if len(p2.coefficients) == 0:
            return p1
        return Polynomial.gcd(p2, Polynomial.divide(p1, p2))