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#ifndef ZMODN_H
#define ZMODN_H
#include <cstdint>
#include <iostream>
#include <optional>
#include <tuple>
#include <type_traits>
template<typename T>
concept Integer = requires(T a, T b, int i, std::ostream& os) {
{T(i)};
{a + b} -> std::same_as<T>;
{a - b} -> std::same_as<T>;
{a * b} -> std::same_as<T>;
{a / b} -> std::same_as<T>;
{a % b} -> std::same_as<T>;
{a == b} -> std::same_as<bool>;
{a != b} -> std::same_as<bool>;
{os << a} -> std::same_as<std::ostream&>;
};
template<Integer T>
std::tuple<T, T, T> extended_gcd(T a, T b) {
if (b == 0) return {a, 1, 0};
auto [g, x, y] = extended_gcd(b, a%b);
return {g, y, x - y*(a/b)};
}
template<Integer auto N>
requires(N > 1)
class Zmod {
public:
Zmod(decltype(N) z) : value{(z%N + N) % N} {}
decltype(N) toint() const { return value; }
Zmod operator+(const Zmod& z) const { return value + z.value; }
Zmod operator-(const Zmod& z) const { return value - z.value; }
Zmod operator*(const Zmod& z) const { return value * z.value; }
Zmod operator+=(const Zmod& z) { return (*this) = value + z.value; }
Zmod operator-=(const Zmod& z) { return (*this) = value - z.value; }
Zmod operator*=(const Zmod& z) { return (*this) = value * z.value; }
Zmod operator^(decltype(N) z) const {
if (z == 0) return 1;
if (z % 2 == 0) return (((*this) * (*this)) ^ (z/2));
return (*this) * ((*this) ^ (z-1));
}
bool operator==(const Zmod& z) const { return value == z.value; }
bool operator!=(const Zmod& z) const { return value != z.value; }
std::optional<Zmod> inverse() const {
auto [g, a, _] = extended_gcd(value, N);
return g == 1 ? Zmod(a) : std::optional<Zmod>{};
}
std::optional<Zmod> operator/(const Zmod& d) const {
auto i = d.inverse();
return i ? (*this) * i.value() : i;
}
std::optional<Zmod> operator/=(const Zmod& d) {
auto q = *this / d;
return q ? (*this = q.value()) : q;
}
friend std::ostream& operator<<(std::ostream& os, const Zmod<N>& z) {
return os << "(" << z.value << " mod " << N << ")";
}
private:
decltype(N) value;
};
#endif
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