根據自己的喜好把求快速冪的方法名從 power(a,b) 改成了q_pow(a,b)

附帶組合數的實現

（拿來吧你）

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 _WIN32uint64_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; #elsevalue = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value)); #endifreturn *this;}template <typename U = T>typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {long long q = static_cast<long long>(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())); }friend const Type& abs(const Modular& x) { return x.value; }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 V, typename U>friend V& operator>>(V& 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> q_pow(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> bool IsZero(const Modular<T>& number) {return number() == 0; }template <typename T> string to_string(const Modular<T>& number) {return to_string(number()); }// U == std::ostream? but done this way because of fastoutput template <typename U, typename T> U& operator<<(U& stream, const Modular<T>& number) {return stream << number(); }// U == std::istream? but done this way because of fastinput template <typename U, typename T> U& operator>>(U& stream, Modular<T>& number) {typename common_type<typename Modular<T>::Type, long long>::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 = (int) 1e9 + 7; using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;vector<Mint> fact(1, 1); vector<Mint> inv_fact(1, 1);Mint C(int n, int k) {if (k < 0 || k > n) {return 0;}while ((int) fact.size() < n + 1) {fact.push_back(fact.back() * (int) fact.size());inv_fact.push_back(1 / fact.back());}return fact[n] * inv_fact[k] * inv_fact[n - k]; }

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