q = 50177

Fq.<yq> = PolynomialRing(ZZ.quotient(q))
Rq = Fq.quotient(yq**256+1, "xq")
xq = Rq.gen()

F2q.<y2q> = PolynomialRing(ZZ.quotient(q*2))
R2q = F2q.quotient(y2q**256+1, "x2q")
x2q = R2q.gen()

F2.<y2> = PolynomialRing(ZZ.quotient(2))
R2 = F2.quotient(y2**256+1, "x2")
x2 = R2.gen()

def center(x, m):
	x = x % m
	if x < m/2:
		return x
	else:
		return x - m

def f(x):
	return (R2([int(i)%2 for i in x.list()]), Rq([int(i)%q for i in x.list()]))

def g(a, b):
	al = a.list()
	bl = b.list()
	return R2q([int(al[i])*q-int(bl[i])*2*(q//2) for i in range(len(al))])

def add(ab, cd):
	return (ab[0]+cd[0], ab[1]+cd[1])

def mul(ab, cd):
	return (ab[0]*cd[0], ab[1]*cd[1])

a = -x2q**2 + 3*x2q + 2
b = 4*x2q + x2q**4
print(g(*mul(f(a), f(b))))
print(a*b)