from secrets import a, b
from collections import namedtuple
from Crypto.Util.number import inverse, bytes_to_long


FLAG = b"crypto{???????????????????????}"

# Create a simple Point class to represent the affine points.
Point = namedtuple("Point", "x y")

# The point at infinity (origin for the group law).
O = 'Origin'


def check_point(P):
    if P == O:
        return True
    else:
        return (P.y**2 - (P.x**3 + a*P.x + b)) % p == 0 and 0 <= P.x < p and 0 <= P.y < p


def point_inverse(P):
    if P == O:
        return P
    return Point(P.x, -P.y % p)


def point_addition(P, Q):
    if P == O:
        return Q
    elif Q == O:
        return P
    elif Q == point_inverse(P):
        return O
    else:
        if P == Q:
            lam = (3*P.x**2 + a)*inverse(2*P.y, p)
            lam %= p
        else:
            lam = (Q.y - P.y) * inverse((Q.x - P.x), p)
            lam %= p
    Rx = (lam**2 - P.x - Q.x) % p
    Ry = (lam*(P.x - Rx) - P.y) % p
    R = Point(Rx, Ry)
    assert check_point(R)
    return R


def double_and_add(P, n):
    Q = P
    R = O
    while n > 0:
        if n % 2 == 1:
            R = point_addition(R, Q)
        Q = point_addition(Q, Q)
        n = n // 2
    assert check_point(R)
    return R


def public_key():
    d = bytes_to_long(FLAG)
    return double_and_add(G, d)


# Define the curve
p = 4368590184733545720227961182704359358435747188309319510520316493183539079703

gx = 8742397231329873984594235438374590234800923467289367269837473862487362482
gy = 225987949353410341392975247044711665782695329311463646299187580326445253608
G = Point(gx, gy)
Q = public_key()

print(Q)