Submission #65512617

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Source Code Expand

// #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<class data_t, data_t _mod>
struct modular_fixed_base{
#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));
	static_assert(1 <= _mod && _mod < data_t(1) << 8 * sizeof(data_t) - 1);
	static constexpr bool VARIATE_MOD_FLAG = false;
	static constexpr data_t mod(){
		return _mod;
	}
	template<class T>
	static constexpr vector<modular_fixed_base> precalc_power(T base, int SZ){
		vector<modular_fixed_base> res(SZ + 1, 1);
		for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
		return res;
	}
	template<class T>
	static constexpr vector<modular_fixed_base> precalc_geometric_sum(T base, int SZ){
		vector<modular_fixed_base> res(SZ + 1);
		for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base + base;
		return res;
	}
	static vector<modular_fixed_base> _INV;
	static constexpr 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_fixed_base _primitive_root;
	static constexpr modular_fixed_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_fixed_base(g).power((_mod - 1) / divs[i]) == 1){
					ok = false;
					break;
				}
			}
			if(ok) return _primitive_root = g;
		}
	}
	constexpr modular_fixed_base(){ }
	constexpr modular_fixed_base(const double &x){ _data = _normalize(llround(x)); }
	constexpr modular_fixed_base(const long double &x){ _data = _normalize(llround(x)); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> constexpr modular_fixed_base(const T &x){ _data = _normalize(x); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> static constexpr data_t _normalize(const T &x){
		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;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> constexpr operator T() const{ return data(); }
	constexpr modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((_data += otr._data) >= _mod) _data -= _mod; return *this; }
	constexpr modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((_data += _mod - otr._data) >= _mod) _data -= _mod; return *this; }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> constexpr modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> constexpr modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); }
	constexpr modular_fixed_base &operator++(){ return *this += 1; }
	constexpr modular_fixed_base &operator--(){ return *this += _mod - 1; }
	constexpr modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }
	constexpr modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }
	constexpr modular_fixed_base operator-() const{ return modular_fixed_base(_mod - _data); }
	constexpr modular_fixed_base &operator*=(const modular_fixed_base &rhs){
		if constexpr(is_same_v<data_t, unsigned int>) _data = (unsigned long long)_data * rhs._data % _mod;
		else 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(_data * rhs._data);
		return *this;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	constexpr modular_fixed_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_fixed_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>
	constexpr modular_fixed_base power(T e) const{
		return modular_fixed_base(*this).inplace_power(e);
	}
	// c + c * x + ... + c * x^{e-1}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	constexpr modular_fixed_base &inplace_geometric_sum(T e, modular_fixed_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_fixed_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>
	constexpr modular_fixed_base geometric_sum(T e, modular_fixed_base c = 1) const{
		return modular_fixed_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
	constexpr optional<data_t> log(const modular_fixed_base &b) const{
		data_t m = mod(), n = sqrtl(m) + 1, j = 1;
		modular_fixed_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 {};
	}
	constexpr optional<modular_fixed_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_fixed_base{u};
	}
	modular_fixed_base &operator/=(const modular_fixed_base &otr){
		auto inv_ptr = otr.inverse();
		assert(inv_ptr);
		return *this = *this * *inv_ptr;
	}
#define ARITHMETIC_OP(op, apply_op)\
constexpr modular_fixed_base operator op(const modular_fixed_base &x) const{ return modular_fixed_base(*this) apply_op x; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
constexpr modular_fixed_base operator op(const T &x) const{ return modular_fixed_base(*this) apply_op modular_fixed_base(x); }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
constexpr friend modular_fixed_base operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x) apply_op y; }
	ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=)
#undef ARITHMETIC_OP
#define COMPARE_OP(op)\
constexpr bool operator op(const modular_fixed_base &x) const{ return _data op x._data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
constexpr bool operator op(const T &x) const{ return _data op modular_fixed_base(x)._data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
constexpr friend bool operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_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_fixed_base &number){
		long long x;
		in >> x;
		number._data = modular_fixed_base::_normalize(x);
		return in;
	}
	friend ostream &operator<<(ostream &out, const modular_fixed_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;
	constexpr data_t data() const{ return _data; }
#undef IS_INTEGRAL
#undef IS_UNSIGNED
};
template<class data_t, data_t _mod> vector<modular_fixed_base<data_t, _mod>> modular_fixed_base<data_t, _mod>::_INV;
template<class data_t, data_t _mod> modular_fixed_base<data_t, _mod> modular_fixed_base<data_t, _mod>::_primitive_root;

constexpr unsigned int mod = (119 << 23) + 1; // 998244353
// constexpr unsigned int mod = 1e9 + 7; // 1000000007
// constexpr unsigned int mod = 1e9 + 9; // 1000000009
// constexpr unsigned long long mod = (unsigned long long)1e18 + 9;
using modular = modular_fixed_base<decay_t<decltype(mod)>, mod>;

constexpr 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);
	auto solve_testcase = [&](auto testcase_id)->int{
		int _n, _h, _w;
		cin >> _n >> _h >> _w;
		if(_h < 2 * _n || _w < 2 * _n){
			cout << "0\n";
			return 0;
		}
		modular n = _n, h = _h, w = _w;
		modular res = 0;
		for(auto rep = 2; rep; -- rep){
			// horizontal split
			modular cur =
				(h - 2 * n + 1).power(2) *
				(h - 2 * n + 2).power(2) *
				(w - 2 * n + 1) *
				(w - 2 * n + 2) *
				((w - 2 * n).power(2) + 3 * (w - 2 * n) + 3) /
				24;
			debug(h, w, cur);
			res += cur;
			swap(h, w);
		}
		{ // subtract double split
			modular cur =	
				(h - 2 * n + 1) *
				(h - 2 * n + 2) *
				((h - 2 * n).power(2) + 3 * (h - 2 * n) + 3) *
				(w - 2 * n + 1) *
				(w - 2 * n + 2) *
				((w - 2 * n).power(2) + 3 * (w - 2 * n) + 3) /
				36;
			debug(cur);
			res -= cur;
		}
		{ // entangled case
			modular cur = (h - 2 * n + 3) * (h - 2 * n + 2) * (h - 2 * n + 1) * (h - 2 * n) * (w - 2 * n + 3) * (w - 2 * n + 2) * (w - 2 * n + 1) * (w - 2 * n) / 24 / 24;
			debug(cur);
			res += 2 * cur;
		}
		cout << res << "\n";
		return 0;
	};
	int testcase_count;
	cin >> testcase_count;
	for(auto testcase_id = 0; testcase_id < testcase_count; ++ testcase_id){
		solve_testcase(testcase_id);
	}
	return 0;
}

/*
\sum_{a=n~h-n} \sum_{b=n~w-n} \sum_{c=n~a-1} \sum_{d=n~b-1} (d-n+1) * (h-a-n+1) * (w-b-n+1) * (c-n+1)
*/

Submission Info

Compile Error

Main.cpp: In instantiation of ‘struct modular_fixed_base<unsigned int, 998244353>’:
Main.cpp:222:45:   required from here
Main.cpp:24:75: warning: suggest parentheses around ‘-’ inside ‘<<’ [-Wparentheses]
   24 |         static_assert(1 <= _mod && _mod < data_t(1) << 8 * sizeof(data_t) - 1);
      |                                                        ~~~~~~~~~~~~~~~~~~~^~~
Main.cpp: In instantiation of ‘static constexpr data_t modular_fixed_base<data_t, _mod>::_normalize(const T&) [with T = int; typename std::enable_if<((is_integral_v<T> || is_same_v<T, __int128>) || is_same_v<T, __int128 unsigned>)>::type* <anonymous> = 0; data_t = unsigned int; data_t _mod = 998244353]’:
Main.cpp:78:133:   required from ‘main()::<lambda(auto:53)> [with auto:53 = int]’
Main.cpp:290:17:   required from here
Main.cpp:252:11:   in ‘constexpr’ expansion of ‘modular_fixed_base<unsigned int, 998244353>(_n)’
Main.cpp:81:34: warning: comparison of integer expressions of different signedness: ‘unsigned int’ and ‘int’ [-Wsign-compare]
   81 |                 data_t v =  _mod <= sign * x ? sign * x % _mod : sign * x;
      |                             ~~~~~^~~~~~~~~~~
Main.cpp: In instantiation of ‘main()::<lambda(auto:53)> [with auto:53 = int]’:
Main.cpp:290:17:   required from here
Main.cpp:14:28: warning: statement has no effect [-Wunused-value]
   14 |         #define debug(...) 42
      |                            ^~
Main.cpp:263:25: note: in expansion of macro ‘debug’
  263 |                         debug(h, w, cur);
      |                         ^~~~~
Main.cpp:14:28: warning: statement has no effect [-Wunused-value]
   14 |         #define debug(...) 42
      |                            ^~
Main.cpp:276:25: note: in expansion of macro ‘debug’
  276 |                         debug(cur);
      |                         ^~~~~
Main.cpp:14:28: warning: statement has no effect [-Wunused-value]
   14 |         #define debug(...) 42
      |                            ^~
Main.cpp:281:25: note: in expansion of macro ‘debug’
  281 |                         debug(cur);
      |                         ^~~~~
Main.cpp:245:40: warning: unused parameter ‘testcase_id’ [-Wunused-parameter]
  245 |         auto solve_testcase = [&](auto testcase_id)->int{
      |                                   ~~~~~^~~~~~~~~~~

Judge Result