intToPerm, permToInt

constexpr int P = 7;

const auto fac = [] {
  std::array<int, P + 1> f {};
  f[0] = 1;
  for (int i = 1; i <= P; ++i) {
    f[i] = i * f[i - 1];
  }
  return f;
} ();

std::array<int, P> intToPerm(int k) {
  assert(0 <= k && k < fac[P]);
  std::array<int, P> res;
  for (int i = P - 1; i >= 0; --i) {
    int w = k / fac[P - 1 - i] % (P - i);
    res[i] = w;
    for (int j = i + 1; j < P; ++j) {
      if (res[j] >= w) {
        res[j] += 1;
      }
    }
  }
  return res;
}

int permToInt(const std::array<int, P>& a) {
  int res = 0;
  for (int i = 0; i < P; ++i) {
    assert(0 <= a[i] && a[i] < P);
    int small = 0;
    for (int j = i + 1; j < P; ++j) {
      assert(a[i] != a[j]);
      if (a[i] > a[j]) {
        small += 1;
      }
    }
    res += small * fac[P - 1 - i];
  }
  return res;
}