ModInt

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ModInt<1000000007> mi = 0;

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template <int Mod>
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class ModInt {
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public:
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  int n;
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  constexpr ModInt(const int x = 0) noexcept : n((x % Mod + Mod) % Mod) {}
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  constexpr int &value() noexcept { return n; }
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  constexpr const int &value() const noexcept { return n; }
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  constexpr ModInt operator+(const ModInt rhs) const noexcept { return ModInt(*this) += rhs; }
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  constexpr ModInt operator-(const ModInt rhs) const noexcept {    return ModInt(*this) -= rhs;  }
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  constexpr ModInt operator*(const ModInt rhs) const noexcept {    return ModInt(*this) *= rhs;  }
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  constexpr ModInt operator/(const ModInt rhs) const noexcept {    return ModInt(*this) /= rhs;  }
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  constexpr ModInt &operator+=(const ModInt rhs) noexcept {
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    n += rhs.n;
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    if (n >= Mod)
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      n -= Mod;
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    return *this;
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  }
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  constexpr ModInt &operator-=(const ModInt rhs) noexcept {
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    if (n < rhs.n)
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      n += Mod;
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    n -= rhs.n;
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    return *this;
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  }
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  constexpr ModInt &operator*=(const ModInt rhs) noexcept {
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    n = n * rhs.n % Mod;
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    return *this;
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  }
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  constexpr ModInt &operator/=(ModInt rhs) noexcept {
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    int exp = Mod - 2;
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    while (exp) {
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      if (exp % 2)
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        *this *= rhs;
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      rhs *= rhs;
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      exp /= 2;
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    }
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    return *this;
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  }
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  friend std::istream &operator>>(std::istream &_istr, ModInt &rhs) {
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    _istr >> rhs.n;
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    rhs.n = (rhs.n % Mod + Mod) % Mod;
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    return _istr;
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  }
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  friend std::ostream &operator<<(std::ostream &_ostr, const ModInt &rhs) {
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    return _ostr << rhs.n;
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  }
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};