extendedEuclid, crt

using Num_t = long long;

static_assert(std::is_signed_v<Num_t>);

std::pair<Num_t, Num_t> extendedEuclid(Num_t a, Num_t b) {
  Num_t ua = 1; Num_t va = 0;
  Num_t ub = 0; Num_t vb = 1;
  while (b != 0) {
    Num_t t = a / b;
    a -= t * b;
    ua -= t * ub;
    va -= t * vb;
    std::swap(a, b);
    std::swap(ua, ub);
    std::swap(va, vb);
  }
  if (a < 0) {
    ua = -ua;
    va = -va;
  }
  return {ua, va};
}

std::pair<Num_t, Num_t> crt(Num_t x0, Num_t m0, Num_t x1, Num_t m1) { /* m0 * m1 < std::numeric_limits<Num_t>::max() / 2 */
  assert(m0 > 0 && m1 > 0);
  if (m0 < m1) {
    std::swap(x0, x1);
    std::swap(m0, m1);
  }
  x0 %= m0; x1 %= m1;
  auto [t0, t1] = extendedEuclid(m0, m1);
  Num_t g = t0 * m0 + t1 * m1;
  if ((x1 - x0) % g != 0) {
    return {-1, -1};
  }
  Num_t resm = m0 * m1 / g;
  Num_t res = x0 + t0 * ((x1 - x0) / g) % m1 * m0;
  res = (res % resm + resm) % resm;
  return {res, resm};
}

template <typename... Num_ts>
std::pair<Num_t, Num_t> crt(Num_t x0, Num_t m0, Num_t x1, Num_t m1, Num_ts... args) {
  auto [x, m] = crt(x0, m0, x1, m1);
  if (x == -1) {
    return {-1, -1};
  }
  return crt(x, m, args...);
}