#963005 (C++23) No.2688 Cell Proliferation (Hard)

• 問題: No.2688 Cell Proliferation (Hard)
• ユーザー: Aeren
• 提出日時: 2024-03-20 23:29:06
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 1,061 ms / 4,000 ms
• コード長: 33,909 bytes
• コンパイル時間: 3,794 ms
• コンパイル使用メモリ: 268,936 KB
• 実行使用メモリ: 59,104 KB
• 最終ジャッジ日時: 2024-03-20 23:29:29
• 合計ジャッジ時間: 22,083 ms
• ジャッジサーバーID （参考情報）: judge14 / judge15

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,676 KB
testcase_01	AC	2 ms; 6,676 KB
testcase_02	AC	2 ms; 6,676 KB
testcase_03	AC	103 ms; 8,920 KB
testcase_04	AC	1,003 ms; 50,352 KB
testcase_05	AC	512 ms; 30,284 KB
testcase_06	AC	234 ms; 16,716 KB
testcase_07	AC	234 ms; 16,580 KB
testcase_08	AC	991 ms; 49,400 KB
testcase_09	AC	951 ms; 48,552 KB
testcase_10	AC	996 ms; 51,120 KB
testcase_11	AC	992 ms; 49,856 KB
testcase_12	AC	248 ms; 16,696 KB
testcase_13	AC	1,061 ms; 59,096 KB
testcase_14	AC	932 ms; 47,064 KB
testcase_15	AC	1,051 ms; 59,104 KB
testcase_16	AC	888 ms; 46,916 KB
testcase_17	AC	505 ms; 31,612 KB
testcase_18	AC	1,035 ms; 57,744 KB
testcase_19	AC	510 ms; 31,780 KB
testcase_20	AC	427 ms; 24,764 KB
testcase_21	AC	441 ms; 24,756 KB
testcase_22	AC	503 ms; 31,220 KB
testcase_23	AC	442 ms; 25,716 KB
testcase_24	AC	1,020 ms; 51,020 KB
testcase_25	AC	165 ms; 16,872 KB
testcase_26	AC	713 ms; 58,112 KB
testcase_27	AC	335 ms; 31,836 KB
testcase_28	AC	729 ms; 46,964 KB

ソースコード

// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#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(_mod >= 1);
	static constexpr bool VARIATE_MOD_FLAG = false;
	static constexpr data_t 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;
		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(){ }
	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)>::type* = nullptr> modular_fixed_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){
		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> 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)>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::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){
		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>
	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>
	modular_fixed_base power(T e) const{
		return modular_fixed_base(*this).inplace_power(e);
	}
	modular_fixed_base &operator/=(const modular_fixed_base &otr){
		make_signed_t<data_t> a = otr.data, m = _mod, u = 0, v = 1;
		if(a < _INV.size()) return *this *= _INV[a];
		while(a){
			make_signed_t<data_t> t = m / a;
			m -= t * a; swap(a, m);
			u -= t * v; swap(u, v);
		}
		assert(m == 1);
		return *this *= u;
	}
#define ARITHMETIC_OP(op, apply_op)\
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>\
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>\
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)\
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>\
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>\
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;
	}
#define _SHOW_FRACTION
	friend ostream &operator<<(ostream &out, const modular_fixed_base &number){
		out << number.data;
	#if defined(LOCAL) && defined(_SHOW_FRACTION)
		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;
#undef _SHOW_FRACTION
#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;

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

// T must be of modular type
// mod must be a prime
// Requires modular
template<class T>
struct number_theoric_transform_wrapper{
	// i \in [2^k, 2^{k+1}) holds w_{2^k+1}^{i-2^k}
	static vector<T> root, buffer1, buffer2;
	static void adjust_root(int n){
		if(root.empty()) root = {1, 1};
		for(auto k = (int)root.size(); k < n; k <<= 1){
			root.resize(n, 1);
			T w = T::primitive_root().power((T::mod() - 1) / (k << 1));
			for(auto i = k; i < k << 1; ++ i) root[i] = i & 1 ? root[i >> 1] * w : root[i >> 1];
		}
	}
	// n must be a power of two
	// p must have next n memories allocated
	// O(n * log(n))
	static void transform(int n, T *p, bool invert = false){
		assert(n && __builtin_popcount(n) == 1 && (T::mod() - 1) % n == 0);
		for(auto i = 1, j = 0; i < n; ++ i){
			int bit = n >> 1;
			for(; j & bit; bit >>= 1) j ^= bit;
			j ^= bit;
			if(i < j) swap(p[i], p[j]);
		}
		adjust_root(n);
		for(auto len = 1; len < n; len <<= 1) for(auto i = 0; i < n; i += len << 1) for(auto j = 0; j < len; ++ j){
			T x = p[i + j], y = p[len + i + j] * root[len + j];
			p[i + j] = x + y, p[len + i + j] = x - y;
		}
		if(invert){
			reverse(p + 1, p + n);
			T inv_n = T(1) / n;
			for(auto i = 0; i < n; ++ i) p[i] *= inv_n;
		}
	}
	static void transform(vector<T> &p, bool invert = false){
		transform((int)p.size(), p.data(), invert);
	}
	// Double the length of the ntt array
	// n must be a power of two
	// p must have next 2n memories allocated
	// O(n * log(n))
	static void double_up(int n, T *p){
		assert(n && __builtin_popcount(n) == 1 && (T().mod() - 1) % (n << 1) == 0);
		buffer1.resize(n << 1);
		for(auto i = 0; i < n; ++ i) buffer1[i << 1] = p[i];
		transform(n, p, true);
		adjust_root(n << 1);
		for(auto i = 0; i < n; ++ i) p[i] *= root[n | i];
		transform(n, p);
		for(auto i = 0; i < n; ++ i) buffer1[i << 1 | 1] = p[i];
		copy(buffer1.begin(), buffer1.begin() + 2 * n, p);
	}
	static void double_up(vector<T> &p){
		int n = (int)p.size();
		p.resize(n << 1);
		double_up(n, p.data());
	}
	// O(n * m)
	static vector<T> convolute_naive(const vector<T> &p, const vector<T> &q){
		vector<T> res(max((int)p.size() + (int)q.size() - 1, 0));
		for(auto i = 0; i < (int)p.size(); ++ i) for(auto j = 0; j < (int)q.size(); ++ j) res[i + j] += p[i] * q[j];
		return res;
	}
	// O((n + m) * log(n + m))
	static vector<T> convolute(const vector<T> &p, const vector<T> &q){
		if(min(p.size(), q.size()) < 55) return convolute_naive(p, q);
		int m = (int)p.size() + (int)q.size() - 1, n = 1 << __lg(m) + 1;
		buffer1.resize(n, 0);
		copy(p.begin(), p.end(), buffer1.begin());
		transform(buffer1);
		buffer2.resize(n, 0);
		copy(q.begin(), q.end(), buffer2.begin());
		transform(buffer2);
		for(auto i = 0; i < n; ++ i) buffer1[i] *= buffer2[i];
		transform(buffer1, true);
		return vector<T>(buffer1.begin(), buffer1.begin() + m);
	}
	// O((n + m) * log(n + m))
	static vector<T> square(const vector<T> &p){
		if((int)p.size() < 40) return convolute_naive(p, p);
		int m = 2 * (int)p.size() - 1, n = 1 << __lg(m) + 1;
		buffer1.resize(n, 0);
		copy(p.begin(), p.end(), buffer1.begin());
		transform(buffer1);
		for(auto i = 0; i < n; ++ i) buffer1[i] *= buffer1[i];
		transform(buffer1, true);
		return vector<T>(buffer1.begin(), buffer1.begin() + m);
	}
	// O((n + m) * log(n + m))
	static vector<T> arbitrarily_convolute(const vector<T> &p, const vector<T> &q){
		using modular0 = modular_fixed_base<unsigned int, 1045430273>;
		using modular1 = modular_fixed_base<unsigned int, 1051721729>;
		using modular2 = modular_fixed_base<unsigned int, 1053818881>;
		using ntt0 = number_theoric_transform_wrapper<modular0>;
		using ntt1 = number_theoric_transform_wrapper<modular1>;
		using ntt2 = number_theoric_transform_wrapper<modular2>;
		vector<modular0> p0((int)p.size()), q0((int)q.size());
		for(auto i = 0; i < (int)p.size(); ++ i) p0[i] = p[i].data;
		for(auto i = 0; i < (int)q.size(); ++ i) q0[i] = q[i].data;
		auto xy0 = ntt0::convolute(p0, q0);
		vector<modular1> p1((int)p.size()), q1((int)q.size());
		for(auto i = 0; i < (int)p.size(); ++ i) p1[i] = p[i].data;
		for(auto i = 0; i < (int)q.size(); ++ i) q1[i] = q[i].data;
		auto xy1 = ntt1::convolute(p1, q1);
		vector<modular2> p2((int)p.size()), q2((int)q.size());
		for(auto i = 0; i < (int)p.size(); ++ i) p2[i] = p[i].data;
		for(auto i = 0; i < (int)q.size(); ++ i) q2[i] = q[i].data;
		auto xy2 = ntt2::convolute(p2, q2);
		static const modular1 r01 = 1 / modular1(modular0::mod());
		static const modular2 r02 = 1 / modular2(modular0::mod());
		static const modular2 r12 = 1 / modular2(modular1::mod());
		static const modular2 r02r12 = r02 * r12;
		static const T w1 = modular0::mod();
		static const T w2 = w1 * modular1::mod();
		int n = (int)p.size() + (int)q.size() - 1;
		vector<T> res(n);
		for(auto i = 0; i < n; ++ i){
			using ull = unsigned long long;
			ull a = xy0[i].data;
			ull b = (xy1[i].data + modular1::mod() - a) * r01.data % modular1::mod();
			ull c = ((xy2[i].data + modular2::mod() - a) * r02r12.data + (modular2::mod() - b) * r12.data) % modular2::mod();
			res[i] = xy0[i].data + w1 * b + w2 * c;
		}
		return res;
	}
};
template<class T> vector<T> number_theoric_transform_wrapper<T>::root;
template<class T> vector<T> number_theoric_transform_wrapper<T>::buffer1;
template<class T> vector<T> number_theoric_transform_wrapper<T>::buffer2;

using ntt = number_theoric_transform_wrapper<modular>;

// Specialized for FFT
template<class T, class FFT>
struct power_series_base: vector<T>{
#define data (*this)
	power_series_base &_inplace_transform(bool invert = false){
		FFT::transform(data, invert);
		return *this;
	}
	power_series_base _transform(bool invert = false) const{
		return power_series_base(*this)._inplace_transform(invert);
	}
	template<class ...Args>
	power_series_base(Args... args): vector<T>(args...){}
	power_series_base(initializer_list<T> init): vector<T>(init){}
	operator bool() const{
		return find_if(data.begin(), data.end(), [&](const T &x){ return x != T{0}; }) != data.end();
	}
	// Returns \sum_{i=0}^{n-1} a_i/i! * X^i
	static power_series_base EGF(vector<T> a){
		int n = (int)a.size();
		T fact = 1;
		for(auto x = 2; x < n; ++ x) fact *= x;
		fact = 1 / fact;
		for(auto i = n - 1; i >= 0; -- i) a[i] *= fact, fact *= i;
		return power_series_base(a);
	}
	// Returns exp(coef * X).take(n) = \sum_{i=0}^{n-1} coef^i/i! * X^i
	static power_series_base EGF(int n, T coef = 1){
		vector<T> a(n, 1);
		for(auto i = 1; i < n; ++ i) a[i] = a[i - 1] * coef;
		return EGF(a);
	}
	vector<T> EGF_to_seq() const{
		int n = (int)data.size();
		vector<T> seq(n);
		T fact = 1;
		for(auto i = 0; i < n; ++ i){
			seq[i] = data[i] * fact;
			fact *= i + 1;
		}
		return seq;
	}
	power_series_base &inplace_reduce(){
		while(!data.empty() && !data.back()) data.pop_back();
		return *this;
	}
	power_series_base reduce() const{
		return power_series_base(*this).inplace_reduce();
	}
	friend ostream &operator<<(ostream &out, const power_series_base &p){
		if(p.empty()) return out << "{}";
		else{
			out << "{";
			for(auto i = 0; i < (int)p.size(); ++ i){
				out << p[i];
				i + 1 < (int)p.size() ? out << ", " : out << "}";
			}
			return out;
		}
	}
	power_series_base &inplace_take(int n){
		data.erase(data.begin() + min((int)data.size(), n), data.end());
		data.resize(n, T{0});
		return *this;
	}
	power_series_base take(int n) const{
		auto res = vector<T>(data.begin(), data.begin() + min((int)data.size(), n));
		res.resize(n, T{0});
		return res;
	}
	power_series_base &inplace_drop(int n){
		data.erase(data.begin(), data.begin() + min((int)data.size(), n));
		return *this;
	}
	power_series_base drop(int n) const{
		return vector<T>(data.begin() + min((int)data.size(), n), data.end());
	}
	power_series_base &inplace_slice(int l, int r){
		assert(0 <= l && l <= r);
		data.erase(data.begin(), data.begin() + min((int)data.size(), l));
		data.resize(r - l, T{0});
		return *this;
	}
	power_series_base slice(int l, int r) const{
		auto res = vector<T>(data.begin() + min((int)data.size(), l), data.begin() + min((int)data.size(), r));
		res.resize(r - l, T{0});
		return res;
	}
	power_series_base &inplace_reverse(int n){
		data.resize(max(n, (int)data.size()), T{0});
		std::reverse(data.begin(), data.begin() + n);
		return *this;
	}
	power_series_base reverse(int n) const{
		return power_series_base(*this).inplace_reverse(n);
	}
	power_series_base &inplace_shift(int n, T x = T{0}){
		data.insert(data.begin(), n, x);
		return *this;
	}
	power_series_base shift(int n, T x = T{0}) const{
		return power_series_base(*this).inplace_shift(n, x);
	}
	T evaluate(T x) const{
		T res = {};
		for(auto i = (int)data.size() - 1; i >= 0; -- i) res = res * x + data[i];
		return res;
	}
	// Takes mod x^n-1
	power_series_base &inplace_circularize(int n){
		assert(n >= 1);
		for(auto i = n; i < (int)data.size(); ++ i) data[i % n] += data[i];
		data.resize(n, T{0});
		return *this;
	}
	// Takes mod x^n-1
	power_series_base circularize(int n) const{
		return power_series_base(*this).inplace_circularize(n);
	}
	power_series_base operator*(const power_series_base &p) const{
		return FFT::convolute(data, p);
	}
	power_series_base &operator*=(const power_series_base &p){
		return *this = *this * p;
	}
	template<class U>
	power_series_base &operator*=(U x){
		for(auto &c: data) c *= x;
		return *this;
	}
	template<class U>
	power_series_base operator*(U x) const{
		return power_series_base(*this) *= x;
	}
	template<class U>
	friend power_series_base operator*(U x, power_series_base p){
		for(auto &c: p) c = x * c;
		return p;
	}
	// Compute p^e mod x^n - 1.
	template<class U>
	power_series_base &inplace_power_circular(U e, int n){
		assert(n >= 1);
		power_series_base p = *this;
		data.assign(n, 0);
		data[0] = 1;
		for(; e; e >>= 1){
			if(e & 1) (*this *= p).inplace_circularize(n);
			(p *= p).inplace_circularize(n);
		}
		return *this;
	}
	template<class U>
	power_series_base power_circular(U e, int len) const{
		return power_series_base(*this).inplace_power_circular(e, len);
	}
	power_series_base &operator+=(const power_series_base &p){
		data.resize(max(data.size(), p.size()), T{0});
		for(auto i = 0; i < (int)p.size(); ++ i) data[i] += p[i];
		return *this;
	}
	power_series_base operator+(const power_series_base &p) const{
		return power_series_base(*this) += p;
	}
	template<class U>
	power_series_base &operator+=(const U &x){
		if(data.empty()) data.emplace_back();
		data[0] += x;
		return *this;
	}
	template<class U>
	power_series_base operator+(const U &x) const{
		return power_series_base(*this) += x;
	}
	template<class U>
	friend power_series_base operator+(const U &x, const power_series_base &p){
		return p + x;
	}
	power_series_base &operator-=(const power_series_base &p){
		data.resize(max(data.size(), p.size()), T{0});
		for(auto i = 0; i < (int)p.size(); ++ i) data[i] -= p[i];
		return *this;
	}
	power_series_base operator-(const power_series_base &p) const{
		return power_series_base(*this) -= p;
	}
	template<class U>
	power_series_base &operator-=(const U &x){
		if(data.empty()) data.emplace_back();
		data[0] -= x;
		return *this;
	}
	template<class U>
	power_series_base operator-(const U &x) const{
		return power_series_base(*this) -= x;
	}
	template<class U>
	friend power_series_base operator-(const U &x, const power_series_base &p){
		return -p + x;
	}
	power_series_base operator-() const{
		power_series_base res = *this;
		for(auto i = 0; i < data.size(); ++ i) res[i] = T{0} - res[i];
		return res;
	}
	power_series_base &operator++(){
		if(data.empty()) data.push_back(1);
		else ++ data[0];
		return *this;
	}
	power_series_base &operator--(){
		if(data.empty()) data.push_back(-1);
		else -- data[0];
		return *this;
	}
	power_series_base operator++(int){
		power_series_base result(*this);
		if(data.empty()) data.push_back(1);
		else ++ data[0];
		return result;
	}
	power_series_base operator--(int){
		power_series_base result(*this);
		if(data.empty()) data.push_back(-1);
		else -- data[0];
		return result;
	}
	power_series_base &inplace_clear_range(int l, int r){
		assert(0 <= l && l <= r);
		for(auto i = l; i < min(r, (int)data.size()); ++ i) data[i] = T{0};
		return *this;
	}
	power_series_base clear_range(int l, int r) const{
		return power_series_base(*this).inplace_clear_range(l, r);
	}
	power_series_base &inplace_dot_product(const power_series_base &p){
		for(auto i = 0; i < min(data.size(), p.size()); ++ i) data[i] *= p[i];
		return *this;
	}
	power_series_base dot_product(const power_series_base &p) const{
		return power_series_base(*this).inplace_power_series_product(p);
	}
	power_series_base &_inverse_doubled_up(power_series_base &f, const power_series_base &freq) const{
		assert((f.size() & -f.size()) == f.size());
		int s = f.size();
		power_series_base buffer = take(s << 1);
		buffer._inplace_transform();
		buffer.inplace_dot_product(freq);
		buffer._inplace_transform(true);
		buffer.inplace_clear_range(0, s);
		buffer._inplace_transform();
		buffer.inplace_dot_product(freq);
		buffer._inplace_transform(true);
		f.resize(s << 1, T{0});
		return f -= buffer.inplace_clear_range(0, s);
	}
	power_series_base &_inverse_doubled_up(power_series_base &f) const{
		assert((f.size() & -f.size()) == f.size());
		return _inverse_doubled_up(f, f.take(f.size() << 1)._transform());
	}
	// Returns the first n terms of the inverse series
	// O(n * log(n))
	power_series_base inverse(int n) const{
		assert(!data.empty() && data[0] != T{0});
		auto inv = 1 / data[0];
		power_series_base res{inv};
		for(auto s = 1; s < n; s <<= 1) _inverse_doubled_up(res);
		res.resize(n, T{0});
		return res;
	}
	// Returns the first n terms of the inverse series
	// O(n * log(n))
	power_series_base &inplace_inverse(int n){
		return *this = this->inverse(n);
	}
	// O(n * log(n))
	power_series_base &inplace_power_series_division(power_series_base p, int n){
		int i = 0;
		while(i < min(data.size(), p.size()) && !data[i] && !p[i]) ++ i;
		data.erase(data.begin(), data.begin() + i);
		p.erase(p.begin(), p.begin() + i);
		(*this *= p.inverse(n)).resize(n, T{0});
		return *this;
	}
	// O(n * log(n))
	power_series_base power_series_division(const power_series_base &p, int n){
		return power_series_base(*this).inplace_power_series_division(p, n);
	}
	// Euclidean division
	// O(min(n * log(n), # of non-zero indices))
	power_series_base &operator/=(const power_series_base &p){
		int n = (int)p.size();
		while(n && p[n - 1] == T{0}) -- n;
		assert(n >= 1);
		inplace_reduce();
		if(data.size() < n){
			data.clear();
			return *this;
		}
		if(n - count(p.begin(), p.begin() + n, T{0}) <= 100){
			T inv = 1 / p[n - 1];
			static vector<int> indices;
			for(auto i = 0; i < n - 1; ++ i) if(p[i]) indices.push_back(i);
			power_series_base res((int)data.size() - n + 1);
			for(auto i = (int)data.size() - 1; i >= n - 1; -- i) if(data[i]){
				T x = data[i] * inv;
				res[i - n + 1] = x;
				for(auto j: indices) data[i - (n - 1 - j)] -= x * p[j];
			}
			indices.clear();
			return *this = res;
		}
		power_series_base b;
		n = data.size() - p.size() + 1;
		b.assign(n, {});
		copy(p.rbegin(), p.rbegin() + min(p.size(), b.size()), b.begin());
		std::reverse(data.begin(), data.end());
		data = FFT::convolute(data, b.inverse(n));
		data.erase(data.begin() + n, data.end());
		std::reverse(data.begin(), data.end());
		return *this;
	}
	power_series_base operator/(const power_series_base &p) const{
		return power_series_base(*this) /= p;
	}
	template<class U>
	power_series_base &operator/=(U x){
		assert(x);
		T inv_x = T(1) / x;
		for(auto &c: data) c *= inv_x;
		return *this;
	}
	template<class U>
	power_series_base operator/(U x) const{
		return power_series_base(*this) /= x;
	}
	pair<power_series_base, power_series_base> divrem(const power_series_base &p) const{
		auto q = *this / p, r = *this - q * p;
		while(!r.empty() && r.back() == 0) r.pop_back();
		return {q, r};
	}
	power_series_base &operator%=(const power_series_base &p){
		int n = (int)p.size();
		while(n && p[n - 1] == T{0}) -- n;
		assert(n >= 1);
		inplace_reduce();
		if(data.size() < n) return *this;
		if(n - count(p.begin(), p.begin() + n, 0) <= 100){
			T inv = 1 / p[n - 1];
			static vector<int> indices;
			for(auto i = 0; i < n - 1; ++ i) if(p[i]) indices.push_back(i);
			for(auto i = (int)data.size() - 1; i >= n - 1; -- i) if(data[i]){
				T x = data[i] * inv;
				data[i] = 0;
				for(auto j: indices) data[i - (n - 1 - j)] -= x * p[j];
			}
			indices.clear();
			return inplace_reduce();
		}
		return *this = this->divrem(p).second;
	}
	power_series_base operator%(const power_series_base &p) const{
		return power_series_base(*this) %= p;
	}
	power_series_base &inplace_derivative(){
		if(!data.empty()){
			for(auto i = 0; i < data.size(); ++ i) data[i] *= i;
			data.erase(data.begin());
		}
		return *this;
	}
	// p'
	power_series_base derivative() const{
		return power_series_base(*this).inplace_derivative();
	}
	power_series_base &inplace_derivative_shift(){
		for(auto i = 0; i < data.size(); ++ i) data[i] *= i;
		return *this;
	}
	// xP'
	power_series_base derivative_shift() const{
		return power_series_base(*this).inplace_derivative_shift();
	}
	power_series_base &inplace_antiderivative(){
		T::precalc_inverse(data.size());
		data.push_back(0);
		for(auto i = (int)data.size() - 1; i >= 1; -- i) data[i] = data[i - 1] / i;
		data[0] = 0;
		return *this;
	}
	// Integral(P)
	power_series_base antiderivative() const{
		return power_series_base(*this).inplace_antiderivative();
	}
	power_series_base &inplace_shifted_antiderivative(){
		T::precalc_inverse(data.size());
		if(!data.empty()) data[0] = 0;
		for(auto i = 1; i < data.size(); ++ i) data[i] /= i;
		return *this;
	}
	// Integral(P/x)
	power_series_base shifted_antiderivative() const{
		return power_series_base(*this).inplace_shifted_antiderivative();
	}
	// O(n * log(n))
	power_series_base &inplace_log(int n){
		assert(!data.empty() && data[0] == 1);
		if(!n){
			data.clear();
			return *this;
		}
		(*this = derivative() * inverse(n)).resize(n - 1, T{0});
		inplace_antiderivative();
		return *this;
	}
	// O(n * log(n))
	power_series_base log(int n) const{
		return power_series_base(*this).inplace_log(n);
	}
	// O(n * log(n))
	power_series_base exp(int n) const{
		assert(data.empty() || data[0] == 0);
		power_series_base f{1}, g{1};
		for(auto s = 1; s < n; s <<= 1){
			power_series_base f2 = f.take(s << 1)._inplace_transform();
			power_series_base g2 = g.take(s << 1)._inplace_transform();
			power_series_base dt = take(s).inplace_derivative_shift();
			power_series_base w = dt;
			w._inplace_transform();
			for(auto i = 0; i < s; ++ i) w[i] *= f2[i << 1];
			w._inplace_transform(true);
			w -= f.derivative_shift();
			w.resize(s << 1, T{0});
			w._inplace_transform();
			w.inplace_dot_product(g2);
			w._inplace_transform(true);
			w.resize(s, T{0});
			w.insert(w.begin(), s, 0);
			w -= dt;
			power_series_base z = take(s << 1);
			z += w.inplace_shifted_antiderivative();
			z._inplace_transform();
			z.inplace_dot_product(f2);
			z._inplace_transform(true);
			f.resize(s << 1, T{0});
			f += z.inplace_clear_range(0, s);
			if(s << 1 < n) f._inverse_doubled_up(g, g2);
		}
		f.resize(n, T{0});
		return f;
	}
	// O(n * log(n))
	power_series_base &inplace_exp(int n){
		return *this = this->exp(n);
	}
	// O(n * log(n))
	template<class U>
	power_series_base &inplace_power(U e, int n){
		data.resize(n, T{0});
		if(e == 0 || n == 0){
			if(n) data[0] = T{1};
			return *this;
		}
		if(e < 0) return inplace_inverse(n).inplace_power(-e, n);
		if(all_of(data.begin(), data.end(), [&](auto x){ return x == T{0}; })) return *this;
		int pivot = find_if(data.begin(), data.end(), [&](auto x){ return x; }) - data.begin();
		if(pivot && e >= (n + pivot - 1) / pivot){
			fill(data.begin(), data.end(), T{0});
			return *this;
		}
		data.erase(data.begin(), data.begin() + pivot);
		n -= pivot * e;
		T pivot_c = T{1}, base = data[0];
		for(auto x = e; x; x >>= 1, base *= base) if(x & 1) pivot_c *= base;
		((*this /= data[0]).inplace_log(n) *= e).inplace_exp(n);
		data.insert(data.begin(), pivot * e, T{0});
		return *this *= pivot_c;
	}
	// O(n * log(n))
	template<class U>
	power_series_base power(U e, int n) const{
		return power_series_base(*this).inplace_power(e, n);
	}
	// Suppose there are data[i] distinct objects with weight i.
	// Returns a power series where i-th coefficient represents # of ways to select a set of objects with sum of weight i.
	// O(n * log(n))
	power_series_base &inplace_set(int n){
		assert(!data.empty() && data[0] == T{0});
		data.resize(n);
		for(auto i = n - 1; i >= 1; -- i) for(auto j = 2 * i; j < n; j += i) data[j] += data[i];
		for(auto i = 1; i < n; ++ i) (data[i] /= i) *= (i & 1 ? 1 : -1);
		return inplace_exp(n);
	}
	power_series_base set(int n) const{
		return power_series_base(*this).inplace_set(n);
	}
	// Suppose there are data[i] distinct objects with weight i.
	// Returns a power series where i-th coefficient represents # of ways to select a multiset of objects with sum of weight i.
	// O(n * log(n))
	power_series_base &inplace_multiset(int n){
		assert(!data.empty() && data[0] == T{0});
		data.resize(n);
		static vector<T> inv;
		inv.resize(n);
		for(auto i = 1; i < n; ++ i) inv[i] = T{1} / i;
		for(auto i = n - 1; i >= 1; -- i) for(auto j = 2 * i; j < n; j += i) data[j] += data[i] * inv[j / i];
		inv.clear(), inv.shrink_to_fit();
		return inplace_exp(n);
	}
	power_series_base multiset(int n) const{
		return power_series_base(*this).inplace_multiset(n);
	}
	static power_series_base multiply_all(const vector<power_series_base> &a){
		if(a.empty()) return {1};
		auto solve = [&](auto self, int l, int r)->power_series_base{
			if(r - l == 1) return a[l];
			int m = l + (r - l >> 1);
			return self(self, l, m) * self(self, m, r);
		};
		return solve(solve, 0, (int)a.size());
	}
	friend power_series_base gcd(power_series_base p, power_series_base q){
		while(q) p = exchange(q, p % q);
		return p;
	}
	friend power_series_base lcm(power_series_base p, power_series_base q){
		return p / gcd(p, q) * q;
	}
#undef data
};

// Requires modular and number_theoric_transform
using power_series = power_series_base<modular, ntt>;

// DEBUG BEGIN
#ifdef LOCAL
// DECLARATION BEGIN
template<class L, class R> ostream &operator<<(ostream &out, const pair<L, R> &p);
template<class Tuple, size_t N> struct _tuple_printer;
template<class... Args> ostream &_print_tuple(ostream &out, const tuple<Args...> &t);
template<class ...Args> ostream &operator<<(ostream &out, const tuple<Args...> &t);
template<class T> ostream &operator<<(typename enable_if<!is_same<T, string>::value, ostream>::type &out, const T &arr);
ostream &operator<<(ostream &out, const _Bit_reference &bit);
template<size_t SZ> ostream &operator<<(ostream &out, const bitset<SZ> &b);
template<class T, class A, class C>
ostream &operator<<(ostream &out, priority_queue<T, A, C> pq);
// DECLARATION END
template<class L, class R> ostream &operator<<(ostream &out, const pair<L, R> &p){
	return out << "{" << p.first << ", " << p.second << "}";
}
template<class Tuple, size_t N> struct _tuple_printer{
	static ostream &_print(ostream &out, const Tuple &t){ return _tuple_printer<Tuple, N-1>::_print(out, t) << ", " << get<N-1>(t); }
};
template<class Tuple> struct _tuple_printer<Tuple, 1>{
	static ostream &_print(ostream &out, const Tuple& t){ return out << get<0>(t); }
};
template<class... Args> ostream &_print_tuple(ostream &out, const tuple<Args...> &t){
	return _tuple_printer<decltype(t), sizeof...(Args)>::_print(out << "{", t) << "}";
}
template<class ...Args> ostream &operator<<(ostream &out, const tuple<Args...> &t){
	return _print_tuple(out, t);
}
template<class T> ostream &operator<<(typename enable_if<!is_same<T, string>::value, ostream>::type &out, const T &arr){
	if(arr.empty()) return out << "{}";
	out << "{";
	for(auto it = arr.begin(); it != arr.end(); ++ it){
		out << *it;
		next(it) != arr.end() ? out << ", " : out << "}";
	}
	return out;
}
ostream &operator<<(ostream &out, const _Bit_reference &bit){
	return out << bool(bit);
}
template<size_t SZ> ostream &operator<<(ostream &out, const bitset<SZ> &b){
	for(auto i = 0; i < SZ; ++ i) out << b[i];
	return out;
}
template<class T, class A, class C>
ostream &operator<<(ostream &out, priority_queue<T, A, C> pq){
	vector<T> a;
	while(!pq.empty()) a.push_back(pq.top()), pq.pop();
	return out << a;
}
template<class Head>
void debug_out(Head H){ cerr << H << endl; }
template<class Head, class... Tail>
void debug_out(Head H, Tail... T){ cerr << H << ", ", debug_out(T...); }
void debug2_out(){ }
template<class Head, class... Tail>
void debug2_out(Head H, Tail... T){ cerr << "\n"; for(auto x: H) cerr << x << ",\n"; debug2_out(T...); }
template<class Width, class Head>
void debugbin_out(Width w, Head H){
	for(auto rep = w; rep; -- rep, H >>= 1) cerr << (H & 1);
	cerr << endl;
}
template<class Width, class Head, class... Tail>
void debugbin_out(Width w, Head H, Tail... T){
	for(auto rep = w; rep; -- rep, H >>= 1) cerr << (H & 1);
	cerr << ", "; debugbin_out(w, T...);
}
enum CODE{ CCRED = 31, CCGREEN = 32, CCYELLOW = 33, CCBLUE = 34, CCDEFAULT = 39 };
#define debug_endl() cerr << endl
#define debug(...) cerr << "\033[" << (int)CODE(CCRED) << "mL" << setw(3) << std::left << __LINE__ << std::right << " [" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debug_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
#define debug2(...) cerr << "\033[" << (int)CODE(CCRED) << "mL" << setw(3) << std::left << __LINE__ << std::right << " [" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debug2_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
#define debugbin(...) cerr << "\033[" << (int)CODE(CCRED) << "mL" << setw(3) << std::left << __LINE__ << std::right << " [" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debugbin_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
#else
#define debug_endl() 42
#define debug(...) 42
#define debug2(...) 42
#define debugbin(...) 42
#endif
// DEBUG END


int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	modular p, q;
	cin >> p;
	{
		int x;
		cin >> x;
		p /= x;
	}
	cin >> q;
	{
		int x;
		cin >> x;
		q /= x;
	}
	int obj;
	cin >> obj;
	power_series f(obj + 1);
	for(auto i = 1; i <= obj; ++ i){
		f[i] = p * q.power(1LL * i * (i - 1) / 2);
	}
	debug(f);
	(f *= (1 - f).inverse(obj + 1)) += 1;
	debug(f);
	modular res = 0;
	for(auto i = 0; i <= obj; ++ i){
		res += f[obj - i] * q.power(1LL * i * (i + 1) / 2);
	}
	cout << res << "\n";
	return 0;
}

/*

*/