#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define Rep(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i ) #define rep(i,n) Rep(i,0,n) #define stop char nyaa;cin>>nyaa; using ll = long long; const int inf = 1e9 + 7; const ll INF = 1LL << 60; //const ll mod = 1e9 + 7; using P = pair; using LP = pair; ll p; typedef vector> mat; typedef vector vec; mat mtmul(mat &A, mat &B) { mat C(A.size(), vec(B[0].size())); rep(i, (int)A.size()) { rep(k, (int)B.size()) { rep(j, (int)B[0].size()) { C[i][j] = (C[i][j] + (A[i][k] * B[k][j]) % p) % p; } } } return C; } mat mtpow(mat A, ll n) { mat B(A.size(), vec(A.size())); rep(i, (int)A.size()) { B[i][i] = 1; } while (n > 0) { if (n&(ll)1)B = mtmul(B, A); A = mtmul(A, A); n >>= 1; } return B; } ll dat(mat A) { ll res = A[0][0] * A[1][1] - A[0][1] * A[1][0]; res = (res%p + p) % p; return res; } ll mod_pow(ll x, ll n) { ll res = 1; while (n > 0) { if (n % 2)res = res * x%p; x = x * x%p; n >>= 1; } return res; } mat invmt(mat A) { ll b = dat(A); mat res = { { A[1][1],p - A[0][1] },{ p - A[1][0],A[0][0] } }; b = mod_pow(b, p - 2); rep(i, 2)rep(j, 2) { res[i][j] = res[i][j] * b%p; } return res; } //a^res=b (mod p) ll ident(ll a, ll b) { if (b == 1)return p - 1; if (p <= 100000) { int tmp = 1; ll cop = a; while (cop != b) { cop = cop * a%p; tmp++; if (tmp > p)return -1; } return tmp; } ll d = sqrt(p); map mp; ll cop = b; ll inva = mod_pow(a, p - 2); for (int y = 0; y < d; y++) { mp[cop] = y; cop = cop * inva%p; } ll spea = mod_pow(a, d); cop = 1; for (int x = 0; x <= d; x++) { if (mp.find(cop) != mp.end()) { ll res = x * d + mp[cop]; res %= (p - 1); return res; } cop = cop * spea%p; } return -1; assert(false); return 0; } ll minp(ll a) { vector ds; for (int i = 1; i <= 100000; i++) { if ((p - 1) % i == 0) { ds.push_back(i); ds.push_back((p - 1) / i); } } sort(ds.begin(), ds.end()); ds.erase(unique(ds.begin(), ds.end()), ds.end()); rep(i, ds.size()) { ll kata = ds[i]; if (mod_pow(a, kata) == 1)return kata; } return p - 1; } void solve() { mat A(2), B(2); cin >> p; rep(i, 2) { A[i].resize(2); rep(j, 2)cin >> A[i][j]; } rep(i, 2) { B[i].resize(2); rep(j, 2)cin >> B[i][j]; } ll da = dat(A), db = dat(B); map mp; if (da == 0) { if (db > 0) { cout << -1 << endl; return; } mat cop = A; if (cop == B) { cout << 1 << endl; return; } mp[cop] = true; int tmp = 1; while (true) { tmp++; cop = mtmul(cop, A); if (mp[cop]) { cout << -1 << endl; return; } if (cop == B) { cout << tmp << endl; return; } mp[cop] = true; } } if (db == 0) { cout << -1 << endl; return; } ll k, e; if (da == 1) { if (db != 1) { cout << -1 << endl; return; } k = 1, e = 1; } else { k = ident(da, db); e = minp(da); } if (k < 0) { cout << -1 << endl; return; } //cout << Z[0][0] << " " << Z[0][1] << " " << Z[1][0] << " " << Z[1][1] << endl; mat ap = mtpow(A, e); mat aa = mtpow(A, k); aa = invmt(aa); mat bp = B; bp = mtmul(bp, aa); int sz = 1000000; map memo; ll ans = (ll)1 << 62; mat invap = invmt(ap); mat X = bp; for (int y = 0; y <= sz; y++) { if (memo.find(X) == memo.end()) { memo[X] = y; } X = mtmul(X, invap); } mat app = mtpow(ap, sz); X = { { 1,0 },{ 0,1 } }; for (ll x = 0; x <= sz; x++) { if (memo.find(X) != memo.end()) { ll cs = x * sz + memo[X]; ans = min(ans, cs); } X = mtmul(X, app); } if (ans == ((ll)1 << 62)) { cout << -1 << endl; return; } cout << ans * (p - 1) + k << endl; } signed main() { solve(); //stop return 0; }