結果

問題 No.2457 Stampaholic (Easy)
ユーザー AerenAeren
提出日時 2023-09-02 02:33:51
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2,696 ms / 4,000 ms
コード長 10,872 bytes
コンパイル時間 4,124 ms
コンパイル使用メモリ 367,304 KB
実行使用メモリ 190,976 KB
最終ジャッジ日時 2024-06-11 09:13:07
合計ジャッジ時間 25,555 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 19
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
#include <x86intrin.h>
using namespace std;
using namespace numbers;

using uint = unsigned int;
template<uint _mod>
struct modular_fixed_base{
	static constexpr uint mod(){
		return _mod;
	}
	template<class T>
	static 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;
	}
	static vector<modular_fixed_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_fixed_base _primitive_root;
	static 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;
		uint divs[20] = {};
		divs[0] = 2;
		int cnt = 1;
		uint 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(): data(){ }
	modular_fixed_base(const double &x){ data = normalize(llround(x)); }
	modular_fixed_base(const long double &x){ data = normalize(llround(x)); }
	template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base(const T &x){ data = normalize(x); }
	template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> static uint normalize(const T &x){
		int sign = x >= 0 ? 1 : -1;
		uint v =  _mod <= sign * x ? sign * x % _mod : sign * x;
		if(sign == -1 && v) v = _mod - v;
		return v;
	}
	const uint &operator()() const{ return data; }
	template<class T> operator T() const{ return data; }
	modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }
	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>::value>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
	template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); }
	modular_fixed_base &operator++(){ return *this += 1; }
	modular_fixed_base &operator--(){ return *this += _mod - 1; }
	modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }
	modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }
	modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); }
	modular_fixed_base &operator*=(const modular_fixed_base &rhs){
		data = (unsigned long long)data * rhs.data % _mod;
		return *this;
	}
	template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr>
	modular_fixed_base &inplace_power(T e){
		if(e < 0) *this = 1 / *this, e = -e;
		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>::value>::type* = nullptr>
	modular_fixed_base power(T e) const{
		return modular_fixed_base(*this).inplace_power(e);
	}
	modular_fixed_base &operator/=(const modular_fixed_base &otr){
		int a = otr.data, m = _mod, u = 0, v = 1;
		if(a < _INV.size()) return *this *= _INV[a];
		while(a){
			int t = m / a;
			m -= t * a; swap(a, m);
			u -= t * v; swap(u, v);
		}
		assert(m == 1);
		return *this *= u;
	}
	uint data;
};
template<uint _mod> vector<modular_fixed_base<_mod>> modular_fixed_base<_mod>::_INV;
template<uint _mod> modular_fixed_base<_mod> modular_fixed_base<_mod>::_primitive_root;
template<uint _mod> bool operator==(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data == rhs.data; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator==(const modular_fixed_base<_mod> &lhs, T rhs){ return lhs == modular_fixed_base<_mod>(rhs); }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator==(T lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) == rhs; }
template<uint _mod> bool operator!=(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return !(lhs == rhs); }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator!=(const modular_fixed_base<_mod> &lhs, T rhs){ return !(lhs == rhs); }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator!=(T lhs, const modular_fixed_base<_mod> &rhs){ return !(lhs == rhs); }
template<uint _mod> bool operator<(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data < rhs.data; }
template<uint _mod> bool operator>(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data > rhs.data; }
template<uint _mod> bool operator<=(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data <= rhs.data; }
template<uint _mod> bool operator>=(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data >= rhs.data; }
template<uint _mod> modular_fixed_base<_mod> operator+(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) += rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator+(const modular_fixed_base<_mod> &lhs, T rhs){ return modular_fixed_base<_mod>(lhs) += rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator+(T lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) += rhs; }
template<uint _mod> modular_fixed_base<_mod> operator-(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) -= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator-(const modular_fixed_base<_mod> &lhs, T rhs){ return modular_fixed_base<_mod>(lhs) -= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator-(T lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) -= rhs; }
template<uint _mod> modular_fixed_base<_mod> operator*(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) *= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator*(const modular_fixed_base<_mod> &lhs, T rhs){ return modular_fixed_base<_mod>(lhs) *= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator*(T lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) *= rhs; }
template<uint _mod> modular_fixed_base<_mod> operator/(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs) { return modular_fixed_base<_mod>(lhs) /= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator/(const modular_fixed_base<_mod> &lhs, T rhs) { return modular_fixed_base<_mod>(lhs) /= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator/(T lhs, const modular_fixed_base<_mod> &rhs) { return modular_fixed_base<_mod>(lhs) /= rhs; }
template<uint _mod> istream &operator>>(istream &in, modular_fixed_base<_mod> &number){
	long long x;
	in >> x;
	number.data = modular_fixed_base<_mod>::normalize(x);
	return in;
}
#define _PRINT_AS_FRACTION
template<uint _mod> ostream &operator<<(ostream &out, const modular_fixed_base<_mod> &number){
#if defined(LOCAL) && defined(_PRINT_AS_FRACTION)
	out << number();
	cerr << "(";
	for(auto d = 1; ; ++ d){
		if((number * d).data <= 1000000){
			cerr << (number * d).data << "/" << d;
			break;
		}
		else if((-number * d).data <= 1000000){
			cerr << "-" << (-number * d).data << "/" << d;
			break;
		}
	}
	cerr << ")";
	return out;
#else
	return out << number();
#endif
}
#undef _PRINT_AS_FRACTION

// const uint mod = 1e9 + 7; // 1000000007
const uint mod = (119 << 23) + 1; // 998244353
// const uint mod = 1e9 + 9; // 1000000009
using modular = modular_fixed_base<mod>;

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	int nr, nc, n, k;
	cin >> nr >> nc >> n >> k;
	if(nr > nc){
		swap(nr, nc);
	}
	auto inv = modular(1) / (nr - (k - 1)) / (nc - (k - 1));
	modular res = 0;
	{
		set<array<int, 2>> done;
		auto update = [&](int x, int y)->void{
			if(done.contains({x, y})){
				return;
			}
			done.insert({x, y});
			auto delta = 1 - (1 - inv * (clamp(x + 1, 0, nr - k + 1) - clamp(x - k + 1, 0, nr - k + 1)) * (clamp(y + 1, 0, nc - k + 1) - clamp(y - k + 1, 0, nc - k + 1))).power(n);
			res += delta;
		};
		for(auto x = 0; x < k; ++ x){
			for(auto y = 0; y < k; ++ y){
				update(x, y);
			}
		}
		for(auto x = 0; x < k; ++ x){
			for(auto y = nc - k; y < nc; ++ y){
				update(x, y);
			}
		}
		for(auto x = nr - k; x < nr; ++ x){
			for(auto y = 0; y < k; ++ y){
				update(x, y);
			}
		}
		for(auto x = nr - k; x < nr; ++ x){
			for(auto y = nc - k; y < nc; ++ y){
				update(x, y);
			}
		}
	}
	if(2 * k <= nr){
		for(auto x = 0; x < k; ++ x){
			res += (1 - (1 - inv * (x + 1) * k).power(n)) * 2 * (nr + nc - 4 * k);
		}
		res += (1 - (1 - inv * k * k).power(n)) * (nr - 2 * k) * (nc - 2 * k);
	}
	else if(2 * k <= nc){
		for(auto x = 0; x < nr; ++ x){
			res += (1 - (1 - inv * (clamp(x + 1, 0, nr - k + 1) - clamp(x - k + 1, 0, nr - k + 1)) * k).power(n)) * (nc - 2 * k);
		}
	}
	cout << res << "\n";
	return 0;
}

/*

*/

////////////////////////////////////////////////////////////////////////////////////////
//                                                                                    //
//                                   Coded by Aeren                                   //
//                                                                                    //
////////////////////////////////////////////////////////////////////////////////////////
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