// #pragma GCC optimize("O3,unroll-loops") #include // #include using namespace std; #if __cplusplus >= 202002L using namespace numbers; #endif template struct modular_fixed_base{ #define IS_INTEGRAL(T) (is_integral_v || is_same_v || is_same_v) #define IS_UNSIGNED(T) (is_unsigned_v || is_same_v) 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 static vector precalc_power(T base, int SZ){ vector res(SZ + 1, 1); for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base; return res; } static vector _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::type* = nullptr> modular_fixed_base(const T &x){ data = _normalize(x); } template::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::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::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); } template::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 = (unsigned long long)data * rhs.data % _mod; else if constexpr(is_same_v){ 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::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::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 a = otr.data, m = _mod, u = 0, v = 1; if(a < _INV.size()) return *this *= _INV[a]; while(a){ make_signed_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::type* = nullptr>\ modular_fixed_base operator op(const T &x) const{ return modular_fixed_base(*this) apply_op modular_fixed_base(x); }\ template::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::type* = nullptr>\ bool operator op(const T &x) const{ return data op modular_fixed_base(x).data; }\ template::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 vector> modular_fixed_base::_INV; template modular_fixed_base modular_fixed_base::_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, mod>; 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; auto power = modular::precalc_power(q, obj); vector dp(obj + 1, vector(obj + 1)); for(auto t = 0; t <= obj; ++ t){ dp[t][0] = 1; } for(auto rem = 1; rem <= obj; ++ rem){ for(auto t = 0; t <= obj - rem; ++ t){ dp[t][rem] = p * dp[0][rem - 1] + power[t + 1] * dp[t + 1][rem - 1]; } } cout << dp[0][obj] << "\n"; return 0; } /* */