#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; } struct Rand{ unsigned x; unsigned y; unsigned z; unsigned w; Rand(void){ x=123456789; y=362436069; z=521288629; w=(unsigned)time(NULL); } Rand(unsigned seed){ x=123456789; y=362436069; z=521288629; w=seed; } inline unsigned get(void){ unsigned t; t = (x^(x<<11)); x=y; y=z; z=w; w = (w^(w>>19))^(t^(t>>8)); return w; } inline double getUni(void){ return get()/4294967296.0; } inline int get(int a){ return (int)(a*getUni()); } inline int get(int a, int b){ return a+(int)((b-a+1)*getUni()); } inline long long get(long long a){ return(long long)(a*getUni()); } inline long long get(long long a, long long b){ return a+(long long)((b-a+1)*getUni()); } inline double get(double a, double b){ return a+(b-a)*getUni(); } inline int getExp(int a){ return(int)(exp(getUni()*log(a+1.0))-1.0); } inline int getExp(int a, int b){ return a+(int)(exp(getUni()*log((b-a+1)+1.0))-1.0); } } ; 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(long long x){ int s=0; int m=0; char f[20]; 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'); } } 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); } unsigned long long HashMap_ullP_L[4]; template struct HashMap{ char*used; KEY*key; VAL*val; int mem; int n; int mask; int init_flag; VAL init_val; HashMap(){ mem = 0; init_flag = 0; } ~HashMap(){ free(); } void expand(int nn){ if(mem >= nn){ return; } if(mem){ free(); } mem = nn; used = new char[nn]; key = new KEY[nn]; val = new VAL[nn]; } void free(){ if(mem){ mem = 0; delete[] used; delete[] key; delete[] val; } } void init(int nn){ int i; n = 1; nn = nn + (nn + 1) / 2; while(n < nn){ n *= 2; } mask = n - 1; expand(n); for(i=(0);i<(n);i++){ used[i] = 0; } init_flag = 0; } void init(int nn, VAL ini){ int i; n = 1; nn = nn + (nn + 1) / 2; while(n < nn){ n *= 2; } mask = n - 1; expand(n); for(i=(0);i<(n);i++){ used[i] = 0; } init_flag = 1; init_val = ini; } inline int getHash(const int a){ unsigned long long d = a; d = (((d * HashMap_ullP_L[0]) >> 32) * HashMap_ullP_L[1]) & mask; return d; } inline int getHash(const unsigned a){ unsigned long long d = a; d = (((d * HashMap_ullP_L[0]) >> 32) * HashMap_ullP_L[1]) & mask; return d; } inline int getHash(const long long a){ unsigned long long d = a; d = (((((d * HashMap_ullP_L[0]) >> 32) * HashMap_ullP_L[1]) >> 32) * HashMap_ullP_L[2]) & mask; return d; } inline int getHash(const unsigned long long a){ unsigned long long d = a; d = (((((d * HashMap_ullP_L[0]) >> 32) * HashMap_ullP_L[1]) >> 32) * HashMap_ullP_L[2]) & mask; return d; } inline int getHash(const pair a){ unsigned long long d = (((unsigned long long)a.first) << 32) + ((unsigned long long)a.second); d = (((((d * HashMap_ullP_L[0]) >> 32) * HashMap_ullP_L[1]) >> 32) * HashMap_ullP_L[2]) & mask; return d; } inline VAL& operator[](const KEY a){ int k = getHash(a); for(;;){ if(used[k]==1 && key[k]==a){ break; } if(used[k]==0){ used[k] = 1; key[k] = a; if(init_flag){ val[k] = init_val; } break; } k = (k+1) & mask; } return val[k]; } inline bool exist(const KEY a){ int k = getHash(a); for(;;){ if(used[k]==1 && key[k]==a){ return true; } if(used[k]==0){ break; } k = (k+1) & mask; } return false; } template inline bool exist(const KEY a, S &res){ int k = getHash(a); for(;;){ if(used[k]==1 && key[k]==a){ res = val[k]; return true; } if(used[k]==0){ break; } k = (k+1) & mask; } return false; } } ; int main(){ wmem = memarr; { int i; int j; int k; Rand rnd; for(i=(0);i<(20);i++){ rnd.get(2); } for(i=(0);i<(4);i++){ for(j=(0);j<(32);j++){ k = rnd.get(1,62); HashMap_ullP_L[i] |= (1ULL << k); } HashMap_ullP_L[i] |= (1ULL << 0); HashMap_ullP_L[i] |= (1ULL << 63); } } long long i; long long res; Modint A; rd(A); Modint B; rd(B); Modint P; rd(P); Modint Q; rd(Q); Modint x; Modint y; Modint t; Matrix mt(2,2); Matrix pw; HashMap,int> hs; hs.init(100000); for(i=(0);i<(100000);i++){ hs[{P,Q}] = i; if(B==0){ t = Q / A; } else{ t = (A*Q - P) / B; } auto Q5VJL1cS = ((Q)); auto e98WHCEY = (( t)); P=Q5VJL1cS; Q=e98WHCEY; } mt = 0; mt[0][0] = A; mt[0][1] = -B; mt[1][0] = 1; for(i=0;;i++){ pw =(pow_L(mt,(i * 100000))); x = pw[0][0] * A + pw[0][1] * 2; y = pw[1][0] * A + pw[1][1] * 2; if(hs.exist({x,y})){ res = i * 100000 + hs[{x,y}] + 1; wt_L(res); wt_L('\n'); break; } } return 0; } // cLay version 20210717-1 [beta] // --- original code --- // #define MD 998244353 // { // ll i, res; // Modint @A, @B, @P, @Q, x, y, t; // Matrix mt(2,2), pw; // HashMap,int> hs; // hs.init(1d5); // // rep(i,1d5){ // hs[{P,Q}] = i; // if(B==0) t = Q / A; // else t = (A*Q - P) / B; // (P, Q) = (Q, t); // } // // mt = 0; // mt[0][0] = A; // mt[0][1] = -B; // mt[1][0] = 1; // // for(i=0;;i++){ // pw = mt ** (i * 1d5); // x = pw[0][0] * A + pw[0][1] * 2; // y = pw[1][0] * A + pw[1][1] * 2; // if(hs.exist({x,y})){ // res = i * 1d5 + hs[{x,y}] + 1; // wt(res); // break; // } // } // // }