#!/usr/bin/env python3
import argparse
import json
import pathlib
import re


def inv(value: int, prime: int) -> int:
    return pow(value % prime, -1, prime)


def int_to_bytes(value: int) -> bytes:
    return value.to_bytes(max(1, (value.bit_length() + 7) // 8), "big")


def recover_slope(share_a: dict, share_b: dict, prime: int) -> int:
    x1, y1 = int(share_a["x"]), int(share_a["y"])
    x2, y2 = int(share_b["x"]), int(share_b["y"])
    return ((y2 - y1) * inv(x2 - x1, prime)) % prime


def recover_secret(share: dict, slope: int, prime: int) -> int:
    return (int(share["y"]) - slope * int(share["x"])) % prime


def main() -> int:
    parser = argparse.ArgumentParser()
    parser.add_argument(
        "export",
        nargs="?",
        default="../public/escrow_export.json",
        help="path to escrow_export.json",
    )
    args = parser.parse_args()

    data = json.loads(pathlib.Path(args.export).read_text())
    prime = int(data["field_prime"])
    calibration = data["calibration_batch"]["shares"]
    production_share = data["quarantine_batch"]["shares"][0]

    slope = recover_slope(calibration[0], calibration[1], prime)
    secret_int = recover_secret(production_share, slope, prime)
    flag = int_to_bytes(secret_int).decode()
    if not re.fullmatch(r"caplag\{[^{}]+\}", flag):
        raise SystemExit("recovered secret is not a caplag flag")
    print(flag)
    return 0


if __name__ == "__main__":
    raise SystemExit(main())