from pwn import remote
from math import gcd
from sympy import mod_inverse
from Crypto.Util.number import long_to_bytes, bytes_to_long

def from_dna(dna: str):
    lookup = {"A": 0, "T": 1, "G": 2, "C": 3}
    result = []
    for i in range(0, len(dna), 4):
        chunk = dna[i:i+4]
        c = 0
        for j, base in enumerate(chunk):
            c |= lookup[base] << (j * 2)
        result.append(chr(c))
    return "".join(result)

def download_flag():
    p.sendline(b"3")
    p.recvuntil(b"?")
    p.sendline(b"Vexillum Rex")
    buf = p.recvuntil(b"?")
    buf = buf.split(b"\n")
    return (buf[2].decode(), int(buf[4].decode()))


with remote("7s6shzivkoaegie7wslgzswa7m-5000-dino-vault.challenge.cscg.live", 443, ssl=True) as p:
    p.recvuntil(b"Exit\n")
    flag_enc, n1 = download_flag()
    _, n2 = download_flag()
    vault_key = gcd(n1, n2)
    transmission_key = n1 // vault_key
    e = 2 ** 16 + 1
    phi = (transmission_key - 1) * (vault_key - 1)
    d = mod_inverse(e, phi)
    ciphertext = bytes_to_long(bytes.fromhex(flag_enc))
    plaintext = pow(ciphertext, d, n1)
    print(from_dna(long_to_bytes(plaintext).decode()))