#pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #pragma GCC optimize("inline") #include using namespace std; #define MD (998244353U) template struct cLtraits_identity{ using type = T; } ; template using cLtraits_try_make_signed = typename conditional< is_integral::value, make_signed, cLtraits_identity >::type; template struct cLtraits_common_type{ using tS = typename cLtraits_try_make_signed::type; using tT = typename cLtraits_try_make_signed::type; using type = typename common_type::type; } ; void*wmem; char memarr[96000000]; template inline auto min_L(S a, T b) -> typename cLtraits_common_type::type{ return (typename cLtraits_common_type::type) a <= (typename cLtraits_common_type::type) b ? a : b; } template inline auto max_L(S a, T b) -> typename cLtraits_common_type::type{ return (typename cLtraits_common_type::type) a >= (typename cLtraits_common_type::type) b ? a : b; } struct Modint{ unsigned val; Modint(){ val=0; } Modint(int a){ val = ord(a); } Modint(unsigned a){ val = ord(a); } Modint(long long a){ val = ord(a); } Modint(unsigned long long a){ val = ord(a); } inline unsigned ord(unsigned a){ return a%MD; } inline unsigned ord(int a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned ord(unsigned long long a){ return a%MD; } inline unsigned ord(long long a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned get(){ return val; } inline Modint &operator++(){ val++; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator--(){ if(val == 0){ val = MD - 1; } else{ --val; } return *this; } inline Modint operator++(int a){ Modint res(*this); val++; if(val >= MD){ val -= MD; } return res; } inline Modint operator--(int a){ Modint res(*this); if(val == 0){ val = MD - 1; } else{ --val; } return res; } inline Modint &operator+=(Modint a){ val += a.val; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator-=(Modint a){ if(val < a.val){ val = val + MD - a.val; } else{ val -= a.val; } return *this; } inline Modint &operator*=(Modint a){ val = ((unsigned long long)val*a.val)%MD; return *this; } inline Modint &operator/=(Modint a){ return *this *= a.inverse(); } inline Modint operator+(Modint a){ return Modint(*this)+=a; } inline Modint operator-(Modint a){ return Modint(*this)-=a; } inline Modint operator*(Modint a){ return Modint(*this)*=a; } inline Modint operator/(Modint a){ return Modint(*this)/=a; } inline Modint operator+(int a){ return Modint(*this)+=Modint(a); } inline Modint operator-(int a){ return Modint(*this)-=Modint(a); } inline Modint operator*(int a){ return Modint(*this)*=Modint(a); } inline Modint operator/(int a){ return Modint(*this)/=Modint(a); } inline Modint operator+(long long a){ return Modint(*this)+=Modint(a); } inline Modint operator-(long long a){ return Modint(*this)-=Modint(a); } inline Modint operator*(long long a){ return Modint(*this)*=Modint(a); } inline Modint operator/(long long a){ return Modint(*this)/=Modint(a); } inline Modint operator-(void){ Modint res; if(val){ res.val=MD-val; } else{ res.val=0; } return res; } inline operator bool(void){ return val!=0; } inline operator int(void){ return get(); } inline operator long long(void){ return get(); } inline Modint inverse(){ int a = val; int b = MD; int u = 1; int v = 0; int t; Modint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += MD; } res.val = u; return res; } inline Modint pw(unsigned long long b){ Modint a(*this); Modint res; res.val = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } inline bool operator==(int a){ return ord(a)==val; } inline bool operator!=(int a){ return ord(a)!=val; } } ; inline Modint operator+(int a, Modint b){ return Modint(a)+=b; } inline Modint operator-(int a, Modint b){ return Modint(a)-=b; } inline Modint operator*(int a, Modint b){ return Modint(a)*=b; } inline Modint operator/(int a, Modint b){ return Modint(a)/=b; } inline Modint operator+(long long a, Modint b){ return Modint(a)+=b; } inline Modint operator-(long long a, Modint b){ return Modint(a)-=b; } inline Modint operator*(long long a, Modint b){ return Modint(a)*=b; } inline Modint operator/(long long a, Modint b){ return Modint(a)/=b; } inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } inline void rd(Modint &x){ int i; rd(i); x=i; } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar_unlocked('-'); } while(s--){ my_putchar_unlocked(f[s]+'0'); } } inline void wt_L(Modint x){ int i; i = (int)x; wt_L(i); } template struct Matrix{ int r; int c; int mem; T*dat; Matrix(){ r=c=mem = 0; } Matrix(const int rr, const int cc){ if(rr == 0 || cc == 0){ r = c = 0; } else{ r = rr; c = cc; } mem = r * c; if(mem > 0){ dat = new T[mem]; } } Matrix(const Matrix &a){ int i; r = a.r; c = a.c; mem = r * c; dat = new T[mem]; for(i=(0);i<(mem);i++){ dat[i] = a.dat[i]; } } ~Matrix(){ if(mem){ delete [] dat; } } void changeSize(const int rr, const int cc){ if(rr==0 || cc==0){ r = c = 0; } else{ r = rr; c = cc; } if(mem < r*c){ if(mem){ delete [] dat; } mem = r*c; dat = new T[mem]; } } Matrix& operator=(const Matrix &a){ int i; int j; r = a.r; c = a.c; j = r * c; changeSize(r,c); for(i=(0);i<(j);i++){ dat[i] = a.dat[i]; } return *this; } Matrix& operator=(const int a){ int i; int j; j = r * c; for(i=(0);i<(j);i++){ dat[i] = 0; } j =min_L(r, c); for(i=(0);i<(j);i++){ dat[i*c+i] = a; } return *this; } Matrix& operator+=(const Matrix &a){ int i; int j; if(r==0 || r!=a.r || c!=a.c){ changeSize(0,0); return *this; } j = r*c; for(i=(0);i<(j);i++){ dat[i] += a.dat[i]; } return *this; } Matrix operator+(const Matrix &a){ return Matrix(*this) += a; } Matrix& operator-=(const Matrix &a){ int i; int j; if(r==0 || r!=a.r || c!=a.c){ changeSize(0,0); return *this; } j = r*c; for(i=(0);i<(j);i++){ dat[i] -= a.dat[i]; } return *this; } Matrix operator-(const Matrix &a){ return Matrix(*this) -= a; } Matrix& operator*=(const Matrix &a){ int i; int j; int k; int x; T*m; if(r==0 || c!=a.r){ changeSize(0,0); return *this; } m = (T*)wmem; x = r * a.c; for(i=(0);i<(x);i++){ m[i] = 0; } for(i=(0);i<(r);i++){ for(k=(0);k<(c);k++){ for(j=(0);j<(a.c);j++){ m[i*a.c+j] += dat[i*c+k] * a.dat[k*a.c+j]; } } } changeSize(r, a.c); for(i=(0);i<(x);i++){ dat[i] = m[i]; } return *this; } Matrix operator*(const Matrix &a){ return Matrix(*this) *= a; } Matrix& operator*=(const int a){ int i; int j; j = r * c; for(i=(0);i<(j);i++){ dat[i] *= a; } return *this; } Matrix& operator*=(const long long a){ int i; int j; j = r * c; for(i=(0);i<(j);i++){ dat[i] *= a; } return *this; } Matrix& operator*=(const double a){ int i; int j; j = r * c; for(i=(0);i<(j);i++){ dat[i] *= a; } return *this; } inline T* operator[](const int a){ return dat+a*c; } } ; template Matrix operator*(const int a, const Matrix &b){ return Matrix(b)*=a; } template Matrix operator*(const Matrix &b, const int a){ return Matrix(b)*=a; } template Matrix operator*(const long long a, const Matrix &b){ return Matrix(b)*=a; } template Matrix operator*(const Matrix &b, const long long a){ return Matrix(b)*=a; } template Matrix operator*(const double a, const Matrix &b){ return Matrix(b)*=a; } template Matrix operator*(const Matrix &b, const double a){ return Matrix(b)*=a; } template inline Matrix pow_L(Matrix a, S b){ int i; int j; Matrix res; res.changeSize(a.r, a.c); res = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } template inline T pow_L(T a, S b){ T res = 1; res = 1; for(;;){ if(b&1){ res *= a; } b >>= 1; if(b==0){ break; } a *= a; } return res; } inline double pow_L(double a, double b){ return pow(a,b); } int S; int T; int K; Modint P1; Modint P2; Modint MA; Modint NA; Modint MB; Modint NB; Matrix mt; Modint sp1[120]; Modint sp2[120]; int main(){ int i; wmem = memarr; int c; Modint res1; Modint res2; Modint p; Modint f; rd(MA); rd(NA); rd(S); rd(MB); rd(NB); rd(T); rd(K); P1 = MA / NA; P2 = MB / NB; mt.changeSize(S+T+1, S+T+1); mt = 0; for(i=(0);i<(S+T);i++){ sp1[i] = ((pow_L(P1,i))) * (1 - P1); } int Q5VJL1cS; cLtraits_try_make_signed::type>::type e98WHCEY; if(S+T==0){ e98WHCEY = 0; } else{ e98WHCEY = sp1[0]; for(Q5VJL1cS=(1);Q5VJL1cS<(S+T);Q5VJL1cS++){ e98WHCEY += sp1[Q5VJL1cS]; } } sp1[S+T] = 1 -e98WHCEY; for(i=(0);i<(S+T);i++){ sp2[i] = ((pow_L(P2,i))) * (1 - P2); } int WYIGIcGE; cLtraits_try_make_signed::type>::type t_ynMSdg; if(S+T==0){ t_ynMSdg = 0; } else{ t_ynMSdg = sp2[0]; for(WYIGIcGE=(1);WYIGIcGE<(S+T);WYIGIcGE++){ t_ynMSdg += sp2[WYIGIcGE]; } } sp2[S+T] = 1 -t_ynMSdg; for(i=(0);i<(S+T+1);i++){ int j; for(j=(0);j<(S+T+1);j++){ int k; for(k=(0);k<(S+T+1);k++){ c = i; if(c != 0 && c != S+T){ c =max_L(0, c - j); } if(c != 0 && c != S+T){ c =min_L(S+T, c + k); } mt[i][c] += sp1[j] * sp2[k]; } } } (mt = pow_L(mt,K)); res1 = mt[S][0]; res2 = mt[S][S+T]; wt_L(res1); wt_L('\n'); wt_L(res2); wt_L('\n'); return 0; } // cLay version 20210611-1 [beta] // --- original code --- // #define MD 998244353 // int S, T, K; // Modint P1, P2, MA, NA, MB, NB; // Matrix mt; // Modint sp1[120], sp2[120]; // { // int c; // Modint res1, res2, p, f; // rd(MA,NA,S,MB,NB,T,K); // P1 = MA / NA; // P2 = MB / NB; // mt.changeSize(S+T+1, S+T+1); // mt = 0; // rep(i,S+T) sp1[i] = (P1 ** i) * (1 - P1); sp1[S+T] = 1 - sum(sp1(S+T)); // rep(i,S+T) sp2[i] = (P2 ** i) * (1 - P2); sp2[S+T] = 1 - sum(sp2(S+T)); // rep(i,S+T+1){ // rep(j,S+T+1) rep(k,S+T+1){ // c = i; // if(c != 0 && c != S+T) c = max(0, c - j); // if(c != 0 && c != S+T) c = min(S+T, c + k); // mt[i][c] += sp1[j] * sp2[k]; // } // } // mt **= K; // res1 = mt[S][0]; // res2 = mt[S][S+T]; // wtLn(res1,res2); // }