from math import ceil, floor, log

e = 17
d = 413
n = 3233
m = 65;

def crypt(m):
    return pow(m, e, n)

def clear(c):
    return pow(c, d, n)

def oracle(c):
    return clear(c) % 2 == 0

def double(c):
    return (c * crypt(2)) % n

def solve(c, lower, upper):
    div = 1
    for i in range(int(log(n, 2)) + 1):
        print(f"{i=} {lower=} {upper=} {div=}")
        div = div * 2
        lower = lower * 2
        upper = upper * 2
        new = (lower + upper) >> 1
        c = double(c)
        if oracle(c):
            upper = new
        else:
            lower = new
    return upper * n // div

for m in range(2, n - 1):
    c = crypt(m)
    r = solve(c, 0, 1)
    print(f"{m=} {c=} {r=}")
    assert(r == m)