#include #define show(x) cerr << #x << " = " << x << endl using namespace std; using ll = long long; using pii = pair; using vi = vector; template ostream& operator<<(ostream& os, const vector& v) { os << "sz=" << v.size() << "\n["; for (const auto& p : v) { os << p << ","; } os << "]\n"; return os; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } constexpr ll MOD = 1e9 + 7; template constexpr T INF = numeric_limits::max() / 100; ll P, R; ll W, H; template T gcd(const T a, const T b) { return (b != 0) ? gcd(b, a % b) : a; } template T extgcd(const T a, const T b, T& x, T& y) // ax+by=gcd(a,b) { T d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } template T inverse(const T a, const T mod) { if (gcd(a, mod) != 1) { // cerr << "No inverse" << endl; return -1; } T x, y; extgcd(a, mod, x, y); return (mod + x % mod) % mod; } template T divide(const T a, const T b, const T mod) // return x (s.t. ax=b)(remark: x is value of modulo (mod/gcd(a, mod))) { const T g = gcd(a, mod); if ((g + b % g) % g != 0) { // cerr << "Cannot divide" << endl; return -1; } else { return (mod + (inverse(a / g, mod / g) * (b / g)) % mod) % mod; } } ll power(const ll a, const ll n) { if (n == 0) { return 1; } if (n % 2 == 0) { const ll p = power(a, n / 2); return (p * p) % P; } else { return (a * power(a, n - 1)) % P; } } unordered_map table; ll step; ll logR(const ll a) // return log_R(a) { if (a == 1) { return 0; } ll val = a; for (ll i = 0; i < W; i++) { if (table.find(val) != table.end()) { return i * H + table[val]; } else { val = (val * step) % P; } } } pair square_root(const ll a) { if (a == 0) { return make_pair(0, 0); } else { if (P % 4 == 3) { const ll s = power(a, (P + 1) / 4); return make_pair(s, P - s); } const ll x2 = logR(a); return make_pair(power(R, x2 / 2), power(R, (x2 + (P - 1)) / 2)); } } bool quadratic(ll n) { if (n == 0) { return true; } else { return power(n, (P - 1) / 2) == 1; } } int main() { cin >> P >> R; ll Q; cin >> Q; ll mini = INF; for (ll i = 1; i * i <= P - 1; i++) { const ll w = i; const ll h = (P - 1 + i - 1) / i; if (mini > h + w * Q) { mini = h + w * Q; H = h; W = w; } } for (ll i = 0; i < H; i++) { table[power(R, i)] = i; } step = power(R, (P - 1) - H); for (ll q = 0; q < Q; q++) { ll A, B, C; cin >> A >> B >> C; if (B != 0 and C != 0) { const ll sq = (P + (B * B - 4 * A * C) % P) % P; if (not quadratic(sq)) { cout << -1 << endl; continue; } const pair root = square_root(sq); ll Z[4]; for (int i = 0; i < 4; i++) { if (i % 2 == 0) { if (i / 2 == 0) { Z[i] = (P + (-B + root.first) % P) % P; } else { Z[i] = (P + (-B + root.second) % P) % P; } } else { if (i / 2 == 0) { Z[i] = (P + (-B - root.first) % P) % P; } else { Z[i] = (P + (-B - root.second) % P) % P; } } } vector X(4); for (int i = 0; i < 4; i++) { if (Z[i] == 0) { X[i] = 0; } else { X[i] = divide(2 * A, Z[i], P); } } sort(X.begin(), X.end()); X.erase(unique(X.begin(), X.end()), X.end()); for (ll i = 0; i < X.size(); i++) { if (i != 0) { cout << " "; } cout << X[i]; } cout << endl; } else if (B != 0) { cout << 0 << " "; const ll b = divide(A, -B, P); cout << b << endl; } else if (C != 0) { const ll x2 = divide(A, -C, P); if (quadratic(x2)) { const pair root = square_root(x2); const ll u = root.first; const ll v = root.second; cout << min(u, v) << " " << max(u, v) << endl; } else { cout << -1 << endl; } } else { cout << 0 << endl; } } return 0; }