#include using namespace std; string to_string(string s) { return '"' + s + '"'; } string to_string(bool b) { return b ? "true" : "false"; } template string to_string(bitset bs) { string res; for (size_t i = 0; i < N; ++i) res += '0' + bs[i]; return res; } string to_string(vector v) { string res = "{"; for (bool e : v) res += to_string(e) + ", "; return res += "}"; } template string to_string(pair p); template string to_string(C c) { string res = "{"; for (auto e : c) res += to_string(e) + ", "; return res += "}"; } template string to_string(pair p) { return "(" + to_string(p.first) + ", " + to_string(p.second) + ")"; } void debug() { cerr << '\n'; } template void debug(Head head, Tail... tail) { cerr << ' ' << to_string(head), debug(tail...); } #ifdef LOCAL #define DEBUG(...) cerr << "[" << #__VA_ARGS__ << "]:", debug(__VA_ARGS__) #else #define DEBUG(...) #endif struct Stopwatch { clock_t t = clock(); void restart() { t = clock(); } int elapsed() const { return (clock() - t) * 1000 / CLOCKS_PER_SEC; } friend string to_string(Stopwatch sw) { return "Time: " + to_string(sw.elapsed()) + " ms"; } } sw; long long mod; struct Mint { long long v; Mint(long long a = 0) : v((a %= mod) < 0 ? a + mod : a) {} Mint& operator*=(Mint r) { v = v * r.v % mod; return *this; } Mint& operator/=(Mint r) { return *this *= r.inv(); } Mint& operator+=(Mint r) { if ((v += r.v) >= mod) v -= mod; return *this; } Mint& operator-=(Mint r) { if ((v -= r.v) < 0) v += mod; return *this; } friend Mint operator*(Mint l, Mint r) { return l *= r; } friend Mint operator/(Mint l, Mint r) { return l /= r; } friend Mint operator+(Mint l, Mint r) { return l += r; } friend Mint operator-(Mint l, Mint r) { return l -= r; } Mint pow(long long n) const { assert(n >= 0); Mint res = 1; for (Mint t = *this; n; t *= t, n >>= 1) if (n & 1) res *= t; return res; } Mint inv() const { assert(v); return pow(mod - 2); } friend string to_string(Mint a) { return to_string(a.v); } }; bool operator<(Mint l, Mint r) { return l.v < r.v; } bool operator==(Mint l, Mint r) { return l.v == r.v; } long long tmod(long long a, long long b) { if (b < 0) return -tmod(-a, -b); return (a %= b) < 0 ? a + b : a; } long long tdiv(long long a, long long b) { return (a - tmod(a, b)) / b; } long long mod_pow(long long a, long long n, long long p) { assert(n >= 0); a = tmod(a, p); long long res = 1; while (n) { if (n & 1) (res *= a) %= p; (a *= a) %= p; n >>= 1; } return res; } long long mod_sqrt(long long a, long long p) { if (!a or p == 2) return a; if (mod_pow(a, (p - 1) / 2, p) != 1) { return -1; } long long d = p - 1; while (d % 2 == 0) d /= 2; long long x = mod_pow(a, (d + 1) / 2, p), y = mod_pow(a, d, p), z = -1; for (long long g = 2; g < p; ++g) if (mod_pow(g, (p - 1) / 2, p) != 1) { z = mod_pow(g, d, p); break; } for (int k = __lg((p - 1) / d) - 1; k; --k) { if (mod_pow(y, 1 << (k - 1), p) != 1) { x = x * z % p; y = y * z % p * z % p; } z = z * z % p; } return min(x, p - x); } using Mat = array< array, 2>; Mat mul(Mat A, Mat B) { Mat C{0, 0, 0, 0}; for (int i : {0, 1}) { for (int k : {0, 1}) { for (int j : {0, 1}) { C[i][j] += A[i][k] * B[k][j]; } } } return C; } Mat pow(Mat A, long long n) { Mat res{1, 0, 0, 1}; while (n) { if (n & 1) { res = mul(res, A); } A = mul(A, A); n >>= 1; } return res; } Mat inv(Mat A) { Mat res{ A[1][1], 0 - A[0][1], 0 - A[1][0], A[0][0] }; Mint det = A[0][0] * A[1][1] - A[0][1] * A[1][0]; assert(det.v); for (int i : {0, 1}) { for (int j : {0, 1}) { res[i][j] /= det; } } return res; } long long mat_ord(Mat A) { long long res = mod - 1; for (int i = 2; i * i <= res; ++i) { while (res % i == 0 and pow(A, res / i) == Mat{1, 0, 0, 1}) { res /= i; } } return res; } long long mat_log(Mat A, Mat B) { long long m = ceil(sqrt(mod - 1)); map mp; Mat a{1, 0, 0, 1}; for (int j = 0; j < m; ++j) { mp[a] = j; a = mul(a, A); } A = inv(pow(A, m)), a = {1, 0, 0, 1}; for (long long i = 0; i < (mod - 1 + m - 1) / m; ++i) { if (mp.count(mul(a, B))) { long long res = i * m + mp[mul(a, B)]; if (res == 0) { res = mat_ord(A); } return res; } a = mul(a, A); } return -1; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); cin >> mod; Mat A, B; for (int i : {0, 1}) { for (int j : {0, 1}) { cin >> A[i][j].v; } } for (int i : {0, 1}) { for (int j : {0, 1}) { cin >> B[i][j].v; } } int n = 1; Mat C = A; while (sw.elapsed() < 1000) { if (C == B) { cout << n << '\n'; return 0; } C = mul(C, A); ++n; } if (mod < n) { cout << "-1\n"; return 0; } Mint tr = A[0][0] + A[1][1]; Mint det = A[0][0] * A[1][1] - A[0][1] * A[1][0]; auto t = mod_sqrt((tr * tr - 4 * det).v, mod); assert(t != -1); assert(t != 0); assert(det.v); cout << mat_log(A, B) << '\n'; }