取模运算类（ModIntBase）

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;

/**   取模运算类（ModIntBase）
 *    2024-08-14: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=70980889&returnHomeType=1&uid=329687984
 *    2024-10-11: https://qoj.ac/submission/629765
**/
// TODO: Dynamic ModInt
using u32 = unsigned; using i64 = long long; using u64 = unsigned long long; 

template<typename T>
constexpr T power(T a, u64 b) {
    T res {1};
    for (; b != 0; b /= 2, a *= a) {
        if (b % 2 == 1) {
            res *= a;
        }
    }
    return res;
}
 
template<u32 P>
constexpr u32 mulMod(u32 a, u32 b) {
    return 1ULL * 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;
}
 
template<typename U, U P>
// requires std::unsigned_integral<U>
struct ModIntBase {
public:
    constexpr ModIntBase() : x(0) {}
    
    template<typename T>
    // requires std::integral<T>
    constexpr ModIntBase(T x_) : x(norm(x_ % T {P})) {}
     
    constexpr static U norm(U x) {
        if ((x >> (8 * sizeof(U) - 1) & 1) == 1) {
            x += P;
        }
        if (x >= P) {
            x -= P;
        }
        return x;
    }
     
    constexpr U val() const {
        return x;
    }
     
    constexpr ModIntBase operator-() const {
        ModIntBase res;
        res.x = norm(P - x);
        return res;
    }
     
    constexpr ModIntBase inv() const {
        return power(*this, P - 2);
    }
     
    constexpr ModIntBase &operator*=(const ModIntBase &rhs) & {
        x = mulMod<P>(x, rhs.val());
        return *this;
    }
     
    constexpr ModIntBase &operator+=(const ModIntBase &rhs) & {
        x = norm(x + rhs.x);
        return *this;
    }
     
    constexpr ModIntBase &operator-=(const ModIntBase &rhs) & {
        x = norm(x - rhs.x);
        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::ostream &operator<<(std::ostream &os, const ModIntBase &a) {
        return os << a.val();
    }
     
    friend constexpr bool operator==(ModIntBase lhs, ModIntBase rhs) {
        return lhs.val() == rhs.val();
    }
     
    friend constexpr bool operator!=(ModIntBase lhs, ModIntBase rhs) {
        return lhs.val() != rhs.val();
    }
     
    friend constexpr bool operator<(ModIntBase lhs, 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>;
 
constexpr u32 P = 1000000007;
using Z = ModInt<P>;