#include using namespace std; #define fst(t) std::get<0>(t) #define snd(t) std::get<1>(t) #define thd(t) std::get<2>(t) using ll = long long; template T expt(T a, T n, T mod = std::numeric_limits::max()); template T inverse(T n, T mod); std::tuple extgcd(ll a, ll b); ll ti; ll B; ll P, R; ll n, alpha; std::vector> expos; ll table[252521]; const int dx[8] = {-1, 1, 0, 0, -1, -1, 1, 1}, dy[8] = {0, 0, -1, 1, -1, 1, -1, 1}; void init(); ll babyStepGiantStep(ll b); int main(int argc, char** argv){ std::cin.tie(nullptr); std::ios::sync_with_stdio(false); ti = 12; scanf("%lld %lld", &P, &R); init(); ll g, s; tie(g, s, ignore) = extgcd(2ll, P-1); int Q; scanf("%d", &Q); for(int i=0;i= 0 ? D : D + P; ll sq; if(D == 0){ sq = 0; }else{ ll m = babyStepGiantStep(D); if(m == -1){ puts("-1"); continue; } ll t = s * (m / g) % (P - 1); t = t >= 0 ? t : t + (P - 1); sq = expt(R, t, P); } ll den = inverse(2ll * a % P, P); ll x0 = (-b - sq) * den % P, x1 = (-b + sq) * den % P; x0 = x0 >= 0 ? x0 : x0 + P; x1 = x1 >= 0 ? x1 : x1 + P; if(x0 > x1){swap(x0, x1);} if(x0 == x1){ printf("%lld\n", x0); }else{ printf("%lld %lld\n", x0, x1); } } } void init(){ B = (int)sqrt(P) * ti; n = P / B; alpha = expt(R, B, P); ll inv_alpha = inverse(alpha, P), R_sq = R * R % P; expos.resize((B + 1) / 2); expos[0] = std::make_tuple(1ll, 0); for(int i=1;i<(B+1)/2;++i){ expos[i] = std::make_tuple(std::get<0>(expos[i-1]) * R_sq % P, i * 2); } std::sort(expos.begin(), expos.end()); table[0] = 1ll; for(int i=1;i<=n;++i){ table[i] = table[i-1] * inv_alpha % P; } } // solve a^n = b (in F_p) ll babyStepGiantStep(ll b){ for(int i=0;i<=n;++i){ ll v = b * table[i] % P; auto it = std::lower_bound(expos.begin(), expos.end(), std::make_tuple(v, 0), [](const auto& lhs, const auto& rhs){return std::get<0>(lhs) < std::get<0>(rhs);}); if(it != expos.end() && std::get<0>(*it) == v){ ll c = B * i + std::get<1>(*it); return c; } } return -1ll; } std::tuple extgcd(ll a, ll b){ if(b == 0){ return std::make_tuple(a, 1ll, 0ll); } auto s = extgcd(b, a % b); return std::make_tuple(fst(s), thd(s), snd(s)-(a/b)*thd(s)); } template T expt(T a, T n, T mod){ T res = 1; while(n){ if(n & 1){res = res * a % mod;} a = a * a % mod; n >>= 1; } return res; } template inline T inverse(T n, T mod){ return expt(n, mod-2, mod); }