modint自动取模
modint
自动取模类模板
简单的一种
template <typename T>
concept Can_bit = requires(T x) { x >>= 1; };
template <int MOD>
struct modint {
int val;
static int norm(const int& x) { return x < 0 ? x + MOD : x; }
static constexpr int get_mod() { return MOD; }
modint inv() const {
assert(val);
int a = val, b = MOD, u = 1, v = 0, t;
while (b > 0) t = a / b, swap(a -= t * b, b), swap(u -= t * v, v);
assert(b == 1);
return modint(u);
}
modint() : val(0) {}
modint(const int& m) : val(norm(m)) {}
modint(const long long& m) : val(norm(m % MOD)) {}
modint operator-() const { return modint(norm(-val)); }
bool operator==(const modint& o) { return val == o.val; }
bool operator<(const modint& o) { return val < o.val; }
modint& operator+=(const modint& o) { return val = (1ll * val + o.val) % MOD, *this; }
modint& operator-=(const modint& o) { return val = norm(1ll * val - o.val), *this; }
modint& operator*=(const modint& o) { return val = static_cast<int>(1ll * val * o.val % MOD), *this; }
modint& operator/=(const modint& o) { return *this *= o.inv(); }
modint& operator^=(const modint& o) { return val ^= o.val, *this; }
modint& operator>>=(const modint& o) { return val >>= o.val, *this; }
modint& operator<<=(const modint& o) { return val <<= o.val, *this; }
modint operator-(const modint& o) const { return modint(*this) -= o; }
modint operator+(const modint& o) const { return modint(*this) += o; }
modint operator*(const modint& o) const { return modint(*this) *= o; }
modint operator/(const modint& o) const { return modint(*this) /= o; }
modint operator^(const modint& o) const { return modint(*this) ^= o; }
modint operator>>(const modint& o) const { return modint(*this) >>= o; }
modint operator<<(const modint& o) const { return modint(*this) <<= o; }
friend std::istream& operator>>(std::istream& is, modint& a) {
long long v;
return is >> v, a.val = norm(v % MOD), is;
}
friend std::ostream& operator<<(std::ostream& os, const modint& a) { return os << a.val; }
friend std::string tostring(const modint& a) { return std::to_string(a.val); }
template <Can_bit T>
friend modint qpow(const modint& a, const T& b) {
assert(b >= 0);
modint x = a, res = 1;
for (T p = b; p; x *= x, p >>= 1)
if (p & 1) res *= x;
return res;
}
};
using M107 = modint<1000000007>;
using M998 = modint<998244353>;
using Mint = M107;
// constexpr mod = ...;
// using Mint = modint<mod>;
struct Fact {
std::vector<Mint> fact, factinv;
const int n;
Fact(const int& _n) : n(_n), fact(_n + 1, Mint(1)), factinv(_n + 1) {
for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
factinv[n] = fact[n].inv();
for (int i = n; i; --i) factinv[i - 1] = factinv[i] * i;
}
Mint C(const int& n, const int& k) {
if (n < 0 || k < 0 || n < k) return 0;
return fact[n] * factinv[k] * factinv[n - k];
}
Mint A(const int& n, const int& k) {
if (n < 0 || k < 0 || n < k) return 0;
return fact[n] * factinv[n - k];
}
};
By tourist
template <typename T>
T inv(const T& x, const T& y) {
assert(x != 0);
T u = 0, v = 1, a = x, m = y, t;
while (a != 0) {
t = m / a;
swap(a, m -= t * a);
swap(u -= t * v, 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 = static_cast<Type>((-mod() <= x && x < mod()) ? x : 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, 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(inv(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> qpow(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
for (T p = b; p; x *= x, p >>= 1)
if (p & 1) res *= x;
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;// for mod can change
// using Mint = Modular<VarMod>;
constexpr int md = (int)1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
struct Fact {
vector<Mint> fact, factinv;
const int n;
Fact(const int& _n) : n(_n), fact(_n + 1, Mint(1)), factinv(_n + 1) {
for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
factinv[n] = inv(fact[n](), md);
for (int i = n; i; --i) factinv[i - 1] = factinv[i] * i;
}
Mint C(const int& n, const int& k) {
if (n < 0 || k < 0 || n < k) return 0;
return fact[n] * factinv[k] * factinv[n - k];
}
Mint A(const int& n, const int& k) {
if (n < 0 || k < 0 || n < k) return 0;
return fact[n] * factinv[n - k];
}
};
