//#pragma GCC optimize("Ofast") //#pragma GCC target("avx") //#undef LOCAL #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template using V = vector; template using VV = V>; template ostream& operator<<(ostream& os, const pair& p) { return os << "P(" << p.first << ", " << p.second << ")"; } template ostream& operator<<(ostream& os, const V& v) { os << "["; for (auto d : v) os << d << ", "; return os << "]"; } /* int main() { Scanner sc = Scanner(stdin); Printer pr = Printer(stdout); return 0; } */ struct Scanner { FILE* fp = nullptr; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) reread(); return true; } template ::value, int> = 0> bool read_single(T& ref) { if (!succ()) return false; while (true) { succ(); size_t sz = 1; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (st != ed) break; } return true; } template ::value, int> = 0> bool read_single(T& ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] - '0'); } if (neg) ref = -ref; return true; } template bool read_single(V& ref) { for (auto& d : ref) { if (!read_single(d)) return false; } return true; } void read() {} template void read(H& h, T&... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE* _fp) : fp(_fp) {} }; struct Printer { public: template void write() {} template void write(const H& h, const T&... t) { if (F) write_single(' '); write_single(h); write(t...); } template void writeln(const T&... t) { write(t...); write_single('\n'); } Printer(FILE* _fp) : fp(_fp) {} ~Printer() { flush(); } private: static constexpr size_t SIZE = 1 << 15; FILE* fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write_single(const char& val) { if (pos == SIZE) flush(); line[pos++] = val; } template ::value, int> = 0> void write_single(const T& val) { for (char c : val) write_single(c); } template ::value, int> = 0> void write_single(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write_single('0'); return; } if (val < 0) { write_single('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char('0' + (val % 10)); val /= 10; } reverse(small, small + len); memcpy(line + pos, small, len); pos += len; } template void write_single(const V& val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write_single(' '); write_single(val[i]); } } }; #include Scanner sc = Scanner(stdin); Printer pr = Printer(stdout); using M = array, 2>; ll md; M e() { M m = M{}; m[0][0] = m[1][1] = 1; return m; } ll det(M a) { ll x = (a[0][0] * a[1][1] - a[0][1] * a[1][0]); return (x % md + md) % md; } M mul(M a, M b) { M c = M(); for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { for (int k = 0; k < 2; k++) { c[i][j] += a[i][k] * b[k][j]; } c[i][j] %= md; } } return c; } M pow_mod(M x, ll n) { M r = e(); while (n) { if (n & 1) r = mul(r, x); x = mul(x, x); n >>= 1; } return r; } const ll STEP = TEN(5); ll discrete_logarithm_inside(M start, M x, M y) { map mp; M big = e(); // x^m for (ll i = 0; i < STEP; i++) { mp[y] = i; y = mul(y, x); big = mul(big, x); } for (ll step = 0; step < 2 * TEN(10); step += STEP) { start = mul(start, big); // check [step + 1, step + STEP] if (mp.count(start)) { return (step + STEP) - mp[start]; } } return -1; } ll discrete_logarithm(M x, M y) { M start = e(); for (int i = 0; i < 100; i++) { if (i && start == y) return i; start = mul(start, x); } ll pred = 100 + discrete_logarithm_inside(start, x, y); if (pow_mod(x, pred) != y) return -1; return pred; } ll pow_mod(ll x, ll n) { ll r = 1 % md; x %= md; while (n) { if (n & 1) r = (r * x) % md; x = (x * x) % md; n >>= 1; } return r; } ll discrete_logarithm(ll start, ll x, ll y) { auto mul = [&](ll a, ll b) { return (a * b) % md; }; unordered_map mp; ll big = 1; // x^m for (ll i = 0; i < STEP; i++) { mp[y] = i; y = mul(y, x); big = mul(big, x); } for (ll step = 0; step < md + 10; step += STEP) { start = mul(start, big); // check [step + 1, step + STEP] if (mp.count(start)) { return (step + STEP) - mp[start]; } } return -1; } ll discrete_logarithm(ll x, ll y) { if (md == 1) return 0; auto mul = [&](ll a, ll b) { return (a * b) % md; }; ll start = 1; for (int i = 0; i < 100; i++) { if (i && start == y) return i; start = mul(start, x); } ll pred = 100 + discrete_logarithm(start, x, y); if (pow_mod(x, pred) != y) return -1; return pred; } int main() { M a, b; sc.read(md); sc.read(a[0][0], a[0][1], a[1][0], a[1][1]); sc.read(b[0][0], b[0][1], b[1][0], b[1][1]); ll da = det(a), db = det(b); if (da <= 1) { if (da != db) pr.writeln(-1); else { assert(da != 1); pr.writeln(discrete_logarithm(a, b)); } return 0; } // da ^ x = db ll x = discrete_logarithm(da, db); if (x == -1) { pr.writeln(-1); return 0; } M a2 = pow_mod(a, x); ll u = (a2 == b) ? 0 : discrete_logarithm_inside(a2, pow_mod(a, md - 1), b); if (u != -1) u = (u * (md - 1)) + x; pr.writeln(u); return 0; }