#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; template struct modint { private: unsigned int value; static constexpr int mod() {return m;} public: constexpr modint(const long long x = 0) noexcept { long long y = x; if(y < 0 || y >= mod()) { y %= mod(); if(y < 0) y += mod(); } value = (unsigned int)y; } static constexpr int get_mod() noexcept {return m;} static constexpr int primitive_root() noexcept { assert(m == 998244353); return 3; } constexpr unsigned int val() noexcept {return value;} constexpr modint &operator+=(const modint &other) noexcept { value += other.value; if(value >= mod()) value -= mod(); return *this; } constexpr modint &operator-=(const modint &other) noexcept { unsigned int x = value; if(x < other.value) x += mod(); x -= other.value; value = x; return *this; } constexpr modint &operator*=(const modint &other) noexcept { unsigned long long x = value; x *= other.value; value = (unsigned int) (x % mod()); return *this; } constexpr modint &operator/=(const modint &other) noexcept { return *this *= other.inverse(); } constexpr modint inverse() const noexcept { assert(value); long long a = value,b = mod(),x = 1,y = 0; while(b) { long long q = a/b; a -= q*b; swap(a,b); x -= q*y; swap(x,y); } return modint(x); } constexpr modint power(long long N) const noexcept { assert(N >= 0); modint p = *this,ret = 1; while(N) { if(N & 1) ret *= p; p *= p; N >>= 1; } return ret; } constexpr modint operator+() {return *this;} constexpr modint operator-() {return modint() - *this;} constexpr modint &operator++(int) noexcept {return *this += 1;} constexpr modint &operator--(int) noexcept {return *this -= 1;} friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;} friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;} friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;} friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;} friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;} }; using mint = modint<998244353>; /* using mint = modint<1000000007>; */ template struct Matrix { private: vector> M; int H,W; public: static const Matrix e(int N) { Matrix ret(N,N); for(int i = 0;i < N;i++) ret[i][i] = 1; return ret; }; constexpr Matrix(int h,int w,T x = 0) noexcept { H = h,W = w; M.assign(H,vector(W,x)); } constexpr vector &operator[](const int i) noexcept { assert(0 <= i && i < H); return M[i]; } constexpr vector operator[](const int i) const { assert(0 <= i && i < H); return M[i]; } constexpr Matrix &operator*=(const Matrix &rhs) noexcept { assert(W == rhs.H); Matrix tmp(H,rhs.W); for(int i = 0;i < H;i++) { for(int j = 0;j < rhs.W;j++) { for(int k = 0;k < W;k++) { tmp[i][j] += M[i][k] * rhs.M[k][j]; } } } swap(*this,tmp); return *this; } constexpr Matrix power(long long N) noexcept { assert(H == W); assert(N >= 0); Matrix res = e(H),P = *this; while(N) { if(N & 1) res *= P; P *= P; N >>= 1; } return res; }; friend Matrix operator*(const Matrix &lhs,const Matrix &rhs) { return Matrix(lhs) *= rhs; } friend ostream &operator<<(ostream &os,const Matrix &x) { for(int i = 0;i < x.H;i++) { for(int j = 0;j < x.W;j++) { os << x.M[i][j] << (i + 1 < x.H && j + 1 == x.W ? "\n":" "); } } return os; } }; /* using mat = Matrix; */ void Main() { mint P,Q; int S,T; { int M,N; cin >> M >> N >> S; P = mint(M) / N; } { int M,N; cin >> M >> N >> T; Q = mint(M) / N; } vector X(110),Y(110); X[0] = Y[0] = 1; for(int i = 1;i < 110;i++) { X[i] = X[i - 1] * P; Y[i] = Y[i - 1] * Q; } int K; cin >> K; Matrix M(S + T + 1,S + T + 1); for(int i = -T;i <= S;i++) { if(i == -T || i == S) { M[i + T][i + T] = 1; continue; } for(int j = -T;j <= S;j++) { if(j == S) { M[j + T][i + T] = P.power(S - i); } else if(j == -T) { for(int k = i;k < S;k++) { M[j + T][i + T] += X[k - i] * (1 - P) * Y[k + T]; } } else { for(int k = max(i,j);k < S;k++) { M[j + T][i + T] += X[k - i] * (1 - P) * Y[k - j] * (1 - Q); } } } } Matrix dp(S + T + 1,1); dp[T][0] = 1; dp = M.power(K) * dp; cout << dp[S + T][0] << "\n"; cout << dp[0][0] << "\n"; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int tt = 1; /* cin >> tt; */ while(tt--) Main(); }