#!/usr/bin/env sage
# -*- coding: utf-8 -*-

import re
import sys


def parse_task(path):
    text = open(path, "r", encoding="utf-8").read()

    def pick(name):
        m = re.search(rf"^{name}\s*=\s*([0-9]+)\s*$", text, re.MULTILINE)
        if not m:
            raise RuntimeError(f"cannot find {name} in {path}")
        return Integer(m.group(1))

    N = pick("N")
    e = pick("e")
    c = pick("c")
    p_revealed = pick("p_revealed")
    return N, e, c, p_revealed


def main():
    task_path = sys.argv[1] if len(sys.argv) > 1 else "public/task.txt"
    N, e, c, p_revealed = parse_task(task_path)

    # From src/chal.py
    hidden_bits = 448
    X = 2 ** hidden_bits

    print(f"[*] N bits: {N.nbits()}")
    print(f"[*] hidden bits: {hidden_bits}")
    print("[*] running Coppersmith small_roots...")

    R = Zmod(N)
    P.<x> = PolynomialRing(R)
    f = x + p_revealed

    roots = f.small_roots(X=X, beta=0.4)
    if not roots:
        raise RuntimeError("small_roots found no solution")

    x0 = Integer(roots[0])
    p = Integer(p_revealed + x0)
    if N % p != 0:
        raise RuntimeError("candidate p does not divide N")

    q = Integer(N // p)
    phi = (p - 1) * (q - 1)
    d = Integer(inverse_mod(e, phi))
    m = Integer(power_mod(c, d, N))
    m_int = int(m)
    flag = m_int.to_bytes((m_int.bit_length() + 7) // 8, "big")

    try:
        print(flag.decode("utf-8"))
    except Exception:
        print(flag)


if __name__ == "__main__":
    main()