// https://codeforces.com/blog/entry/96344 #pragma GCC optimize("O3,unroll-loops") #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") #include using namespace std; using ll = long long; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template bool chmax(T& a, const T& b) { bool res = a < b; a = max(a, b); return res; } template bool chmin(T& a, const T& b){ bool res = a > b; a = min(a, b); return res; } typedef vector vl; typedef pair pll; typedef vector> vll; typedef vector vi; typedef vector> vii; typedef pair pii; const int inf = 1000000009; const ll linf = 4000000000000000009; // https://trap.jp/post/1224/ template void input(T&... a){ (cin >> ... >> a); } void print(){ cout << '\n'; } template void print(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } #define rep1(a) for(int i = 0; i < a; i++) #define rep2(i, a) for(int i = 0; i < a; i++) #define rep3(i, a, b) for(int i = a; i < b; i++) #define rep4(i, a, b, c) for(int i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second //--------------------------------- // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); template struct modint{ using mint = modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } modint() : _v(0) {} template modint(T v) { long long x = (long long)(v % (long long)(umod())); if(x < 0) x += umod(); _v = (unsigned int)(x); } unsigned int val() const { return _v; } mint& operator--(){ if(_v == 0) _v = umod(); _v--; return *this; } mint& operator++(){ _v++; if(_v == umod()) _v = 0; return *this; } mint& operator++(int) { mint result = *this; ++*this; return result; } mint& operator--(int){ mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs){ _v += rhs._v; if(_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs){ _v -= rhs._v; if(_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs){ unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = is_prime; }; using modint998244353 = modint<998244353>; using modint1000000007 = modint<1000000007>; using mint = modint998244353; void solve(){ int p1,p2,q1,q2,t; input(p1,p2,q1,q2,t); vector cell(t+1, mint(0)); cell[0] = mint(1); mint c1 = mint(p1)/mint(p2); mint c2 = mint(q1)/mint(q2); vector die(t+1); die[0] = 1; rep(i, 1, t+1) die[i] = die[i-1]*c2; rep(i, 1, t+1){ rep(j, 0, i){ cell[i] += cell[j] * c1; cell[j] *= die[i-j]; } } mint ans = accumulate(cell.begin(), cell.end(), mint(0)); print(ans.val()); } int main(){ ios::sync_with_stdio(false); cin.tie(0); int t = 1; //cin >> t; rep(i,0,t) solve(); }