#1081542 (C++23) No.3133 法B逆元

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問題	No.3133 法B逆元
ユーザー	Aeren
提出日時	2025-05-02 21:26:32
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	11,134 bytes
コンパイル時間	2,919 ms
コンパイル使用メモリ	278,284 KB
実行使用メモリ	6,272 KB
最終ジャッジ日時	2025-05-02 21:26:40
合計ジャッジ時間	3,570 ms
ジャッジサーバーID （参考情報）	judge1 / judge3
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ファイルパターン	結果
other	AC * 21
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ソースコード

raw source code
// #include <bits/allocator.h> // Temp fix for gcc13 global pragma
// #pragma GCC target("avx2,bmi2,popcnt,lzcnt")
// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif
#ifdef LOCAL
	#include "Debug.h"
#else
	#define debug_endl() 42
	#define debug(...) 42
	#define debug2(...) 42
	#define debug_bin(...) 42
#endif

template<int id, class data_t, class wider_data_t>
struct modular_unfixed_base{
#ifdef LOCAL
	#define ASSERT(x) assert(x)
#else
	#define ASSERT(x) 42
#endif
#define IS_INTEGRAL(T) (is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
#define IS_UNSIGNED(T) (is_unsigned_v<T> || is_same_v<T, __uint128_t>)
	static_assert(IS_UNSIGNED(data_t) && IS_UNSIGNED(wider_data_t) && sizeof(data_t) * 2 == sizeof(wider_data_t));
	static constexpr bool VARIATE_MOD_FLAG = true;
	static data_t _mod;
	static wider_data_t _inverse_mod;
	static data_t &mod(){
		return _mod;
	}
	static void precalc_barrett(){
		_inverse_mod = (wider_data_t)-1 / _mod + 1;
	}
	static void setup(data_t mod = 0){
		_primitive_root._data = 0;
		_INV.clear();
		if(!mod) cin >> mod;
		_mod = mod;
		ASSERT(1 <= _mod && _mod < data_t(1) << 8 * sizeof(data_t) - 1);
		precalc_barrett();
	}
	template<class T>
	static vector<modular_unfixed_base> precalc_power(T base, int SZ){
		vector<modular_unfixed_base> res(SZ + 1, 1);
		for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
		return res;
	}
	template<class T>
	static vector<modular_unfixed_base> precalc_geometric_sum(T base, int SZ){
		vector<modular_unfixed_base> res(SZ + 1);
		for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base + base;
		return res;
	}
	static vector<modular_unfixed_base> _INV;
	static void precalc_inverse(int SZ){
		if(_INV.empty()) _INV.assign(2, 1);
		for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);
	}
	// _mod must be a prime
	static modular_unfixed_base _primitive_root;
	static modular_unfixed_base primitive_root(){
		if(_primitive_root) return _primitive_root;
		if(_mod == 2) return _primitive_root = 1;
		if(_mod == 998244353) return _primitive_root = 3;
		data_t divs[20] = {};
		divs[0] = 2;
		int cnt = 1;
		data_t x = (_mod - 1) / 2;
		while(x % 2 == 0) x /= 2;
		for(auto i = 3; 1LL * i * i <= x; i += 2){
			if(x % i == 0){
				divs[cnt ++] = i;
				while(x % i == 0) x /= i;
			}
		}
		if(x > 1) divs[cnt ++] = x;
		for(auto g = 2; ; ++ g){
			bool ok = true;
			for(auto i = 0; i < cnt; ++ i){
				if(modular_unfixed_base(g).power((_mod - 1) / divs[i]) == 1){
					ok = false;
					break;
				}
			}
			if(ok) return _primitive_root = g;
		}
	}
	modular_unfixed_base(){ }
	modular_unfixed_base(const double &x){ _data = _normalize(llround(x)); }
	modular_unfixed_base(const long double &x){ _data = _normalize(llround(x)); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_unfixed_base(const T &x){ _data = _normalize(x); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> static data_t _normalize(const T &x){
		if(_mod == 1) return 0;
		if constexpr(is_same_v<data_t, unsigned int>){
			ASSERT(_inverse_mod);
			int sign = x >= 0 ? 1 : -1;
			data_t v = _mod <= sign * x ? sign * x - ((__uint128_t)(sign * x) * _inverse_mod >> 64) * _mod : sign * x;
			if(v >= _mod) v += _mod;
			if(sign == -1 && v) v = _mod - v;
			return v;
		}
		else{
			int sign = x >= 0 ? 1 : -1;
			data_t v =  _mod <= sign * x ? sign * x % _mod : sign * x;
			if(sign == -1 && v) v = _mod - v;
			return v;
		}
	}
	const data_t &operator()() const{ return _data; }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> operator T() const{ return data(); }
	modular_unfixed_base &operator+=(const modular_unfixed_base &otr){ if((_data += otr._data) >= _mod) _data -= _mod; return *this; }
	modular_unfixed_base &operator-=(const modular_unfixed_base &otr){ if((_data += _mod - otr._data) >= _mod) _data -= _mod; return *this; }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_unfixed_base &operator+=(const T &otr){ return *this += modular_unfixed_base(otr); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_unfixed_base &operator-=(const T &otr){ return *this -= modular_unfixed_base(otr); }
	modular_unfixed_base &operator++(){ return *this += 1; }
	modular_unfixed_base &operator--(){ return *this += _mod - 1; }
	modular_unfixed_base operator++(int){ modular_unfixed_base result(*this); *this += 1; return result; }
	modular_unfixed_base operator--(int){ modular_unfixed_base result(*this); *this += _mod - 1; return result; }
	modular_unfixed_base operator-() const{ return modular_unfixed_base(_mod - _data); }
	modular_unfixed_base &operator*=(const modular_unfixed_base &rhs){
		if constexpr(is_same_v<data_t, unsigned long long>){
			long long res = _data * rhs._data - _mod * (unsigned long long)(1.L / _mod * _data * rhs._data);
			_data = res + _mod * (res < 0) - _mod * (res >= (long long)_mod);
		}
		else _data = _normalize((wider_data_t)_data * rhs._data);
		return *this;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_unfixed_base &inplace_power(T e){
		if(e == 0) return *this = 1;
		if(_data == 0) return *this = {};
		if(_data == 1 || e == 1) return *this;
		if(_data == mod() - 1) return e % 2 ? *this : *this = -*this;
		if(e < 0) *this = 1 / *this, e = -e;
		if(e == 1) return *this;
		modular_unfixed_base res = 1;
		for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
		return *this = res;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_unfixed_base power(T e) const{
		return modular_unfixed_base(*this).inplace_power(e);
	}
	// c + c * x + ... + c * x^{e-1}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_unfixed_base &inplace_geometric_sum(T e, modular_unfixed_base c = 1){
		if(e == 0) return *this = {};
		if(_data == 0) return *this = {};
		if(_data == 1) return *this = c * e;
		if(e == 1) return *this = c;
		if(_data == mod() - 1) return *this = c * abs(e % 2);
		modular_unfixed_base res = 0;
		if(e < 0) return *this = geometric_sum(-e + 1, -*this) - 1;
		if(e == 1) return *this = c * *this;
		for(; e; c *= 1 + *this, *this *= *this, e >>= 1) if(e & 1) res += c, c *= *this;
		return *this = res;
	}
	// c + c * x + ... + c * x^{e-1}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_unfixed_base geometric_sum(T e, modular_unfixed_base c = 1) const{
		return modular_unfixed_base(*this).inplace_geometric_sum(e, c);
	}
	// Returns the minimum integer e>0 with b^e=*this, if it exists
	// O(sqrt(mod)) applications of hashmap
	optional<data_t> log(const modular_unfixed_base &b) const{
		data_t m = mod(), n = sqrtl(m) + 1, j = 1;
		modular_unfixed_base e = 1, f = 1;
		unordered_map<data_t, data_t> A;
		while(j <= n && (f = e *= b) != *this) A[(e * *this).data()] = j ++;
		if(e == *this) return j;
		if(gcd(mod(), e.data()) == gcd(mod(), data())) for(auto i = 2; i < n + 2; ++ i) if(A.count((e *= f).data())) return n * i - A[e.data()];
		return {};
	}
	optional<modular_unfixed_base> inverse() const{
		make_signed_t<data_t> a = data(), m = _mod, u = 0, v = 1;
		if(data() < _INV.size()) return _INV[data()];
		while(a){
			make_signed_t<data_t> t = m / a;
			m -= t * a; swap(a, m);
			u -= t * v; swap(u, v);
		}
		if(m != 1) return {};
		return modular_unfixed_base{u};
	}
	modular_unfixed_base &operator/=(const modular_unfixed_base &otr){
		auto inv_ptr = otr.inverse();
		assert(inv_ptr);
		return *this = *this * *inv_ptr;
	}
#define ARITHMETIC_OP(op, apply_op)\
modular_unfixed_base operator op(const modular_unfixed_base &x) const{ return modular_unfixed_base(*this) apply_op x; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
modular_unfixed_base operator op(const T &x) const{ return modular_unfixed_base(*this) apply_op modular_unfixed_base(x); }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend modular_unfixed_base operator op(const T &x, const modular_unfixed_base &y){ return modular_unfixed_base(x) apply_op y; }
	ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=)
#undef ARITHMETIC_OP
#define COMPARE_OP(op)\
bool operator op(const modular_unfixed_base &x) const{ return _data op x._data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
bool operator op(const T &x) const{ return _data op modular_unfixed_base(x)._data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend bool operator op(const T &x, const modular_unfixed_base &y){ return modular_unfixed_base(x)._data op y._data; }
	COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=)
#undef COMPARE_OP
	friend istream &operator>>(istream &in, modular_unfixed_base &number){
		long long x;
		in >> x;
		number._data = modular_unfixed_base::_normalize(x);
		return in;
	}
	friend ostream &operator<<(ostream &out, const modular_unfixed_base &number){
		out << number._data;
#ifdef LOCAL
		cerr << "(";
		for(auto d = 1; ; ++ d){
			if((number * d)._data <= 1000000){
				cerr << (number * d)._data;
				if(d != 1) cerr << "/" << d;
				break;
			}
			else if((-number * d)._data <= 1000000){
				cerr << "-" << (-number * d)._data;
				if(d != 1) cerr << "/" << d;
				break;
			}
		}
		cerr << ")";
#endif
		return out;
	}
	data_t _data = 0;
	data_t data() const{ return _data; }
#undef ASSERT
#undef IS_INTEGRAL
#undef IS_UNSIGNED
};
template<int id, class data_t, class wider_data_t> data_t modular_unfixed_base<id, data_t, wider_data_t>::_mod;
template<int id, class data_t, class wider_data_t> wider_data_t modular_unfixed_base<id, data_t, wider_data_t>::_inverse_mod;
template<int id, class data_t, class wider_data_t> vector<modular_unfixed_base<id, data_t, wider_data_t>> modular_unfixed_base<id, data_t, wider_data_t>::_INV;
template<int id, class data_t, class wider_data_t> modular_unfixed_base<id, data_t, wider_data_t> modular_unfixed_base<id, data_t, wider_data_t>::_primitive_root;

using modular = modular_unfixed_base<0, unsigned int, unsigned long long>;
// using modular = modular_unfixed_base<0, unsigned long long, __uint128_t>;

modular operator""_m(const char *x){
	modular res = 0;
	long long buffer = 0;
	long long buffer_width = 1;
	constexpr long long buffer_th = 1'000'000'000'000'000'000LL;
	while(*x){
		#ifdef LOCAL
		assert(isdigit(*x));
		#endif
		buffer = buffer * 10 + (*(x ++) - '0');
		if((buffer_width *= 10) == buffer_th){
			res = buffer_width * res + buffer;
			buffer = 0;
			buffer_width = 1;
		}
	}
	res = buffer_width * res + buffer;
	return res;
}

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	unsigned long long n;
	cin >> n;
	modular::setup();
	if(modular::mod() == 1){
		cout << "0\n";
	}
	else if(auto inv_ptr = modular{n}.inverse()){
		cout << *inv_ptr << "\n";
	}
	else{
		cout << "NaN\n";
	}
	return 0;
}

/*

*/
yukicoder

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