text: template <typename T>
  
  T inverse(T a, T m) {
  
    T u = 0, v = 1;
  
    while (a != 0) {
  
      T t = m / a;
  
      m -= t * a; swap(a, m);
  
      u -= t * v; swap(u, v);
  
    }
  
    assert(m == 1);
  
    return u;
  
  }
  
  
  
  template <typename T>
  
  class Modular {
  
   public:
  
    using Type = typename decay<decltype(T::value)>::type;
  
  
  
    constexpr Modular() : value() {}
  
    template <typename U>
  
    Modular(const U& x) {
  
      value = normalize(x);
  
    }
  
  
  
    template <typename U>
  
    static Type normalize(const U& x) {
  
      Type v;
  
      if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
  
      else v = static_cast<Type>(x % mod());
  
      if (v < 0) v += mod();
  
      return v;
  
    }
  
  
  
    const Type& operator()() const { return value; }
  
    template <typename U>
  
    explicit operator U() const { return static_cast<U>(value); }
  
    constexpr static Type mod() { return T::value; }
  
  
  
    Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  
    Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  
    template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  
    template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  
    Modular& operator++() { return *this += 1; }
  
    Modular& operator--() { return *this -= 1; }
  
    Modular operator++(int) { Modular result(*this); *this += 1; return result; }
  
    Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
  
    Modular operator-() const { return Modular(-value); }
  
  
  
    template <typename U = T>
  
    typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
  
  #ifdef _WIN32
  
      uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
  
      uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
  
      asm(
  
        "divl %4; \n\t"
  
        : "=a" (d), "=d" (m)
  
        : "d" (xh), "a" (xl), "r" (mod())
  
      );
  
      value = m;
  
  #else
  
      value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
  
  #endif
  
      return *this;
  
    }
  
    template <typename U = T>
  
    typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
  
      int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
  
      value = normalize(value * rhs.value - q * mod());
  
      return *this;
  
    }
  
    template <typename U = T>
  
    typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
  
      value = normalize(value * rhs.value);
  
      return *this;
  
    }
  
  
  
    Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
  
  
  
    template <typename U>
  
    friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
  
  
  
    template <typename U>
  
    friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
  
  
  
    template <typename U>
  
    friend std::istream& operator>>(std::istream& stream, Modular<U>& number);
  
  
  
   private:
  
    Type value;
  
  };
  
  
  
  template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
  
  template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
  
  template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
  
  
  
  template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
  
  template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
  
  template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
  
  
  
  template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
  
  
  
  template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
  
  template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
  
  template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
  
  
  
  template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
  
  template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
  
  template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
  
  
  
  template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
  
  template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
  
  template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
  
  
  
  template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
  
  template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
  
  template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
  
  
  
  template<typename T, typename U>
  
  Modular<T> power(const Modular<T>& a, const U& b) {
  
    assert(b >= 0);
  
    Modular<T> x = a, res = 1;
  
    U p = b;
  
    while (p > 0) {
  
      if (p & 1) res *= x;
  
      x *= x;
  
      p >>= 1;
  
    }
  
    return res;
  
  }
  
  
  
  template <typename T>
  
  string to_string(const Modular<T>& number) {
  
    return to_string(number());
  
  }
  
  
  
  template <typename T>
  
  std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  
    return stream << number();
  
  }
  
  
  
  template <typename T>
  
  std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  
    typename common_type<typename Modular<T>::Type, int64_t>::type x;
  
    stream >> x;
  
    number.value = Modular<T>::normalize(x);
  
    return stream;
  
  }
  
  
  
  /*
  
  using ModType = int;
  
  
  
  struct VarMod { static ModType value; };
  
  ModType VarMod::value;
  
  ModType& md = VarMod::value;
  
  using Mint = Modular<VarMod>;
  
  */
  
  
  
  constexpr int md = @@HERE@@;
  
  using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;