#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 power(ll p, ll n) { if (n == 0) { return 1; } if (n % 2 == 0) { const ll q = power(p, n / 2); return (q * q) % P; } else { return (p * power(p, n - 1)) % P; } } template pair extgcd(const T x, const T y) // x,y>0 & relatively prime // returns (a,b) s.t. ax+by=1 { ll r0 = x; ll r1 = y; ll a0 = 1; ll a1 = 0; ll b0 = 0; ll b1 = 1; while (r1 > 0) { const ll q1 = r0 / r1; const ll r2 = r0 % r1; const ll a2 = a0 - q1 * a1; const ll b2 = b0 - q1 * b1; r0 = r1; r1 = r2; a0 = a1; a1 = a2; b0 = b1; b1 = b2; } return make_pair(a0 / r0, b0 / r0); } bool quadratic(ll a) { if (a == 0) { return true; } return power(a, (P - 1) / 2) == 1; } ll divide(ll a, ll b, ll mod = P) // b/a { const ll x = (((extgcd(a, mod).first + mod) % mod) * b) % mod; assert((a * x) % mod == b); return x; } template T gcd(const T a, const T b) { return b ? gcd(b, a % b) : a; } mt19937 mt{random_device{}()}; ll rho(ll a) { const ll mod = P - 1; static uniform_int_distribution dist{0, P - 2}; unordered_map> mp; while (true) { const ll alpha = dist(mt); const ll beta = dist(mt); const ll c = (power(a, alpha) * power(R, beta)) % P; if (mp.find(c) != mp.end()) { const auto& p = mp[c]; const ll alpha_ = p.first; const ll beta_ = p.second; if (alpha == alpha_) { continue; } const ll a_ = (((alpha_ - alpha) % mod) + mod) % mod; const ll b_ = (((beta - beta_) % mod) + mod) % mod; const ll g = gcd(a_, b_); const ll x = divide(a_ / g, b_ / g, mod); if (power(R, x) == a) { return x; } } mp[c] = make_pair(alpha, beta); } } ll square_root(ll n) { if (n == 0) { return 0; } if (P % 4 == 3) { return power(n, (P + 1) / 4); } const ll a = rho(n); const ll ind = (a % 2 == 0) ? a / 2 : (a + P) / 2; return power(R, ind); } int main() { cin >> P >> R; ll Q; cin >> Q; for (ll q = 0; q < Q; q++) { ll A, B, C; cin >> A >> B >> C; if (B == 0 and C == 0) { cout << 0 << endl; continue; } const ll elem = (((B * B) % P - (4 * A * C) % P) % P + P) % P; if (not quadratic(elem)) { cout << -1 << endl; continue; } const ll root = square_root(elem); const ll mini = ((-root - B) % P + P) % P; const ll maxi = ((root - B) % P + P) % P; const ll g1 = gcd(2 * A, mini); const ll g2 = gcd(2 * A, maxi); const ll ans1 = divide(2 * A / g1, mini / g1); const ll ans2 = divide(2 * A / g2, maxi / g2); if (ans1 == ans2) { cout << ans1 << endl; } else { cout << min(ans1, ans2) << " " << max(ans1, ans2) << endl; } } return 0; }