#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace { using Integer = long long; //__int128; template istream& operator >> (istream& is, pair& p){return is >> p.first >> p.second;} template istream& operator >> (istream& is, vector& vec){for(T& val: vec) is >> val; return is;} template istream& operator , (istream& is, T& val){ return is >> val;} template ostream& operator << (ostream& os, const pair& p){return os << p.first << " " << p.second;} template ostream& operator << (ostream& os, const vector& vec){for(size_t i=0; i ostream& operator , (ostream& os, const T& val){ return os << " " << val;} template void print(const H& head){ cout << head; } template void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); } template void println(const T& ... values){ print(values...); cout << endl; } template void eprint(const H& head){ cerr << head; } template void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); } template void eprintln(const T& ... values){ eprint(values...); cerr << endl; } class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator end(){ return range_iterator( end_, step_); } }; inline string operator "" _s (const char* str, size_t size){ return move(string(str)); } constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);} constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);} constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); } inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed mt19937 mt(chrono::duration_cast(chrono::steady_clock::now().time_since_epoch()).count()); template string join(const vector& v, const string& sep){ stringstream ss; for(size_t i=0; i0) ss << sep; ss << v[i]; } return ss.str(); } inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; } } long long power_mod(long long x, long long y, long long mod){ long long ret = 1; while(y){ if(y&1) ret = (ret*x) % mod; x = (x*x) % mod; y >>= 1; } return ret; } #include //find k such that x^k = y (mod z) //x and z are co-prime //x^(aH-b) = y (mod z) //x^aH = y * x^b (mod z) long long baby_step_giant_step(long long x, long long y, long long z){ // static long long H = sqrt(z) + 1; static long long H = pow(z, 0.80) + 1; static long long W = z/H + 1; // static set> S; static unordered_map S; if(S.size()==0) for(long long i=0, w=1; i memo; if(memo.count(y)){ return memo[y]; } long long k = -1; static long long x_H = power_mod(x, H, z); long long y_inv = power_mod(y, z-2, z); for(long long i=1, w=x_H * y_inv % z; i<=W; i++, w=(w*x_H)%z){ // auto itr = S.lower_bound({w+1, 0}); // if(itr == S.begin()) continue; // itr--; // if(itr->first == w){ // return H * i - itr->second; // } if( S.count(w) ){ return memo[y] = H*i - S[w]; } } return memo[y] = k; } int main(){ long long p,r; cin >> p,r; long long q; cin >> q; for(int i=0; i> a,b,c; scanf("%lld%lld%lld", &a,&b,&c); long long a2_inv = my_pow_mod(2*a%p, p-2, p); long long b_ = (p-b) % p; long long d = (b*b%p - 4*a%p*c%p) % p; if( d<0 ) d += p; if( d==0 ){ long long x = b_ * a2_inv % p; println(x); continue; } long long w = baby_step_giant_step(r,d, p); if( w%2 != 0 ){ println(-1); continue; } long long xa = (b_ + my_pow_mod(r, w/2, p)) * a2_inv % p; long long xb = (b_ - my_pow_mod(r, w/2, p) + p) * a2_inv % p; if(xa!=xb) println( min(xa,xb), max(xa,xb) ); else println(xa); } return 0; }