快速取模模板

需要C++20及以上，从Jiangly那偷得（bushi

using i64 = long long;
using u64 = unsigned long long;
using u32 = unsigned;
 
using u128 = unsigned __int128;
using i128 = __int128;
 
 
template<class T>
constexpr T power(T a, u64 b, T res = 1) {
    for (; b != 0; b /= 2, a *= a) {
        if (b & 1) {
            res *= a;
        }
    }
    return res;
}
 
template<u32 P>
constexpr u32 mulMod(u32 a, u32 b) {
    return u64(a) * b % P;
}
 
template<u64 P>
constexpr u64 mulMod(u64 a, u64 b) {
    u64 res = a * b - u64(1.L * a * b / P - 0.5L) * P;
    res %= P;
    return res;
}
 
constexpr i64 safeMod(i64 x, i64 m) {
    x %= m;
    if (x < 0) {
        x += m;
    }
    return x;
}
 
constexpr std::pair<i64, i64> invGcd(i64 a, i64 b) {
    a = safeMod(a, b);
    if (a == 0) {
        return {b, 0};
    }
     
    i64 s = b, t = a;
    i64 m0 = 0, m1 = 1;
 
    while (t) {
        i64 u = s / t;
        s -= t * u;
        m0 -= m1 * u;
         
        std::swap(s, t);
        std::swap(m0, m1);
    }
     
    if (m0 < 0) {
        m0 += b / s;
    }
     
    return {s, m0};
}
 
template<std::unsigned_integral U, U P>
struct ModIntBase {
public:
    constexpr ModIntBase() : x(0) {}
    template<std::unsigned_integral T>
    constexpr ModIntBase(T x_) : x(x_ % mod()) {}
    template<std::signed_integral T>
    constexpr ModIntBase(T x_) {
        using S = std::make_signed_t<U>;
        S v = x_ % S(mod());
        if (v < 0) {
            v += mod();
        }
        x = v;
    }
     
    constexpr static U mod() {
        return P;
    }
     
    constexpr U val() const {
        return x;
    }
     
    constexpr ModIntBase operator-() const {
        ModIntBase res;
        res.x = (x == 0 ? 0 : mod() - x);
        return res;
    }
     
    constexpr ModIntBase inv() const {
        return power(*this, mod() - 2);
    }
     
    constexpr ModIntBase &operator*=(const ModIntBase &rhs) & {
        x = mulMod<mod()>(x, rhs.val());
        return *this;
    }
    constexpr ModIntBase &operator+=(const ModIntBase &rhs) & {
        x += rhs.val();
        if (x >= mod()) {
            x -= mod();
        }
        return *this;
    }
    constexpr ModIntBase &operator-=(const ModIntBase &rhs) & {
        x -= rhs.val();
        if (x >= mod()) {
            x += mod();
        }
        return *this;
    }
    constexpr ModIntBase &operator/=(const ModIntBase &rhs) & {
        return *this *= rhs.inv();
    }
     
    friend constexpr ModIntBase operator*(ModIntBase lhs, const ModIntBase &rhs) {
        lhs *= rhs;
        return lhs;
    }
    friend constexpr ModIntBase operator+(ModIntBase lhs, const ModIntBase &rhs) {
        lhs += rhs;
        return lhs;
    }
    friend constexpr ModIntBase operator-(ModIntBase lhs, const ModIntBase &rhs) {
        lhs -= rhs;
        return lhs;
    }
    friend constexpr ModIntBase operator/(ModIntBase lhs, const ModIntBase &rhs) {
        lhs /= rhs;
        return lhs;
    }
     
    friend constexpr std::istream &operator>>(std::istream &is, ModIntBase &a) {
        i64 i;
        is >> i;
        a = i;
        return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const ModIntBase &a) {
        return os << a.val();
    }
     
    friend constexpr bool operator==(const ModIntBase &lhs, const ModIntBase &rhs) {
        return lhs.val() == rhs.val();
    }
    friend constexpr std::strong_ordering operator<=>(const ModIntBase &lhs, const ModIntBase &rhs) {
        return lhs.val() <=> rhs.val();
    }
     
private:
    U x;
};
 
template<u32 P>
using ModInt = ModIntBase<u32, P>;
template<u64 P>
using ModInt64 = ModIntBase<u64, P>;
 
struct Barrett {
public:
    Barrett(u32 m_) : m(m_), im((u64)(-1) / m_ + 1) {}
 
    constexpr u32 mod() const {
        return m;
    }
 
    constexpr u32 mul(u32 a, u32 b) const {
        u64 z = a;
        z *= b;
         
        u64 x = u64((u128(z) * im) >> 64);
         
        u32 v = u32(z - x * m);
        if (m <= v) {
            v += m;
        }
        return v;
    }
 
private:
    u32 m;
    u64 im;
};
 
template<u32 Id>
struct DynModInt {
public:
    constexpr DynModInt() : x(0) {}
    template<std::unsigned_integral T>
    constexpr DynModInt(T x_) : x(x_ % mod()) {}
    template<std::signed_integral T>
    constexpr DynModInt(T x_) {
        int v = x_ % int(mod());
        if (v < 0) {
            v += mod();
        }
        x = v;
    }
     
    constexpr static void setMod(u32 m) {
        bt = m;
    }
     
    static u32 mod() {
        return bt.mod();
    }
     
    constexpr u32 val() const {
        return x;
    }
     
    constexpr DynModInt operator-() const {
        DynModInt res;
        res.x = (x == 0 ? 0 : mod() - x);
        return res;
    }
     
    constexpr DynModInt inv() const {
        auto v = invGcd(x, mod());
        assert(v.first == 1);
        return v.second;
    }
     
    constexpr DynModInt &operator*=(const DynModInt &rhs) & {
        x = bt.mul(x, rhs.val());
        return *this;
    }
    constexpr DynModInt &operator+=(const DynModInt &rhs) & {
        x += rhs.val();
        if (x >= mod()) {
            x -= mod();
        }
        return *this;
    }
    constexpr DynModInt &operator-=(const DynModInt &rhs) & {
        x -= rhs.val();
        if (x >= mod()) {
            x += mod();
        }
        return *this;
    }
    constexpr DynModInt &operator/=(const DynModInt &rhs) & {
        return *this *= rhs.inv();
    }
     
    friend constexpr DynModInt operator*(DynModInt lhs, const DynModInt &rhs) {
        lhs *= rhs;
        return lhs;
    }
    friend constexpr DynModInt operator+(DynModInt lhs, const DynModInt &rhs) {
        lhs += rhs;
        return lhs;
    }
    friend constexpr DynModInt operator-(DynModInt lhs, const DynModInt &rhs) {
        lhs -= rhs;
        return lhs;
    }
    friend constexpr DynModInt operator/(DynModInt lhs, const DynModInt &rhs) {
        lhs /= rhs;
        return lhs;
    }
     
    friend constexpr std::istream &operator>>(std::istream &is, DynModInt &a) {
        i64 i;
        is >> i;
        a = i;
        return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const DynModInt &a) {
        return os << a.val();
    }
     
    friend constexpr bool operator==(const DynModInt &lhs, const DynModInt &rhs) {
        return lhs.val() == rhs.val();
    }
    friend constexpr std::strong_ordering operator<=>(const DynModInt &lhs, const DynModInt &rhs) {
        return lhs.val() <=> rhs.val();
    }
     
private:
    u32 x;
    static Barrett bt;
};

constexpr int MOD[] = {998244353,1000000007};

template<u32 Id>
Barrett DynModInt<Id>::bt = MOD[1];
 
using Z = ModInt<MOD[1]>;