#include #include namespace my{ using namespace std; #define eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define FO(n) for(ll ij=n;ij--;) #define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);isync_with_stdio(0);cout<>(istream&i,ulll&x){ull t;i>>t;x=t;return i;} ostream&operator<<(ostream&o,const ulll&x){return(x<10?o:o<>(istream&i,lll&x){ll t;i>>t;x=t;return i;} ostream&operator<<(ostream&o,const lll&x){return o<0?x:-x);} auto range(bool s,ll a,ll b=1e18,ll c=1){if(b==1e18)b=a,(s?b:a)=0;return array{a-s,b,c};} constexpr char nl=10; constexpr char sp=32; lll pw(lll x,ll n,ll m=0){assert(n>=0);lll r=1;while(n)n&1?r*=x:r,x*=x,m?r%=m,x%=m:r,n>>=1;return r;} constexpr ll pw2(ll n){return 1LL<auto max(const A&...a){return max(initializer_list>{a...});} templateauto min(const A&...a){return min(initializer_list>{a...});} templatestruct pair{ A a;B b; pair()=default; pair(A a,B b):a(a),b(b){} pair(const std::pair&p):a(p.first),b(p.second){} auto operator<=>(const pair&)const=default; friend ostream&operator<<(ostream&o,const pair&p){return o<>auto&sort(auto&a,const F&f={}){ranges::sort(a,f);return a;} auto pop_back(auto&a){assert(a.size());auto r=*a.rbegin();a.pop_back();return r;} templateostream&operator<<(ostream&o,const std::pair&p){return o<ostream&operator<<(ostream&o,const unordered_map&m){fe(m,e)o<concept vectorial=is_base_of_v,V>; templatestruct core_type{using type=T;}; templatestruct core_type{using type=typename core_type::type;}; templateusing core_t=core_type::type; templateistream&operator>>(istream&i,vector&v){fe(v,e)i>>e;return i;} templateostream&operator<<(ostream&o,const vector&v){fe(v,e)o<?nl:sp);return o;} templatestruct vec:vector{ using vector::vector; vec(const vector&v){vector::operator=(v);} vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;} vec operator^(const vec&u)const{return vec{*this}^=u;} vec&operator++(){fe(*this,e)++e;return*this;} vec&operator--(){fe(*this,e)--e;return*this;} auto scan(const auto&f)const{pair,bool>r{};fe(*this,e)if constexpr(!vectorial)r.b?f(r.a,e),r:r={e,1};else if(auto s=e.scan(f);s.b)r.b?f(r.a,s.a),r:r=s;return r;} auto max()const{return scan([](auto&a,const auto&b){ab?a=b:0;;}).a;} }; templatestruct infinity{ templateconstexpr operator T()const{return numeric_limits::max()*(1-is_negative*2);} templateconstexpr operator T()const{return static_cast(*this);} templateconstexpr bool operator==(T x)const{return static_cast(*this)==x;} constexpr auto operator-()const{return infinity();} templateconstexpr operator pair()const{return pair{*this,*this};} }; constexpr infinity oo; void lin(auto&...a){(cin>>...>>a);} templatevoid pp(const auto&...a){ll n=sizeof...(a);((cout<0,c)),...);cout<auto rle(const vec&a){vec>r;fe(a,e)r.size()&&e==r.back().a?++r.back().b:r.eb(e,1).b;return r;} templateauto rce(veca){return rle(sort(a));} ll rand(ll l=oo,ll r=oo){if(l!=oo&&r==oo)r=l,l=0;static ll a=495;a^=a<<7,a^=a>>9;ll t=a;return l>64; return r>=N?r-N:r; } auto&operator+=(const montgomery64&b){if((a+=b.a)>=N)a-=N;return*this;} auto&operator-=(const montgomery64&b){if(i64(a-=b.a)<0)a+=N;return*this;} auto&operator*=(const montgomery64&b){a=reduce(u128(a)*b.a);return*this;} auto&operator/=(const montgomery64&b){*this*=b.inv();return*this;} auto operator+(const montgomery64&b)const{return montgomery64(*this)+=b;} auto operator-(const montgomery64&b)const{return montgomery64(*this)-=b;} auto operator*(const montgomery64&b)const{return montgomery64(*this)*=b;} auto operator/(const montgomery64&b)const{return montgomery64(*this)/=b;} bool operator==(const montgomery64&b)const{return a==b.a;} auto operator-()const{return montgomery64()-montgomery64(*this);} montgomery64 pow(u128 n)const{ montgomery64 r{1},x{*this}; while(n){ if(n&1)r*=x; x*=x; n>>=1; } return r; } montgomery64 inv()const{ u64 a=this->a,b=N,u=1,v=0; while(b)u-=a/b*v,swap(u,v),a-=a/b*b,swap(a,b); return u; } u64 val()const{ return reduce(a); } friend istream&operator>>(istream&i,montgomery64&b){ ll t;i>>t;b=t; return i; } friend ostream&operator<<(ostream&o,const montgomery64&b){ return o<bool miller_rabin(ll n,vecas){ ll d=n-1; while(~d&1)d>>=1; if((ll)modular::mod()!=n)modular::set_mod(n); modular one=1,minus_one=n-1; fe(as,a){ if(a%n==0)continue; ll t=d; modular y=modular(a).pow(t); while(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1; if(y!=minus_one&&~t&1)return 0; } return 1; } bool is_prime(ll n){ if(~n&1)return n==2; if(n<=1)return 0; if(n<4759123141LL)return miller_rabin(n,{2,7,61}); return miller_rabin(n,{2,325,9375,28178,450775,9780504,1795265022}); } templatell pollard_rho(ll n){ if(~n&1)return 2; if(is_prime(n))return n; if((ll)modular::mod()!=n)modular::set_mod(n); modular R,one=1; auto f=[&](const modular&x){return x*x+R;}; while(1){ modular x,y,ys,q=one; R=rand(2,n),y=rand(2,n); ll g=1; constexpr ll m=128; for(ll r=1;g==1;r<<=1){ x=y; fo(r)y=f(y); for(ll k=0;g==1&&k{}; ll d=pollard_rho(m); return d==m?vec{d}:f(f,d)^f(f,m/d); }; return rce(f(f,n)); } templateT mod(T a,T m){return(a%=m)<0?a+m:a;} templateT gcd(T a,T b){return b?gcd(b,a%b):a>0?a:-a;} templateauto gcd(const A&...a){common_type_tr=0;((r=gcd(r,a)),...);return r;} templatepairax_by_g(T a,T b){ if(b==0)return{1,0}; auto[s,t]=ax_by_g(b,a%b); return{t,s-a/b*t}; } ll inv_mod(ll a,ll m){ assert(gcd(a,m)==1); auto[x,y]=ax_by_g(a,m); return mod(x,m); } templateT chinese_remainder_theorem_coprime(const vec&a,vec&m,T M=0){ ll K=a.size(); m.eb(M); vect(K),S(K+1),P(K+1,1); fo(i,K){ t[i]=mod((a[i]-S[i])*inv_mod(P[i],m[i]),m[i]); fo(j,i+1,K+1){ S[j]+=t[i]*P[j]; P[j]*=m[i]; if(m[j])S[j]%=m[j],P[j]%=m[j]; } } ll r=S.back(); m.pop_back(); return S.back(); } templateT chinese_remainder_theorem(const vec&a,const vec&m,T M=0){ ll K=a.size(); fo(i,K)fo(j,i+1,K)if((a[i]-a[j])%gcd(m[i],m[j]))return-1; unordered_map>exponent_max_congruence; fo(i,K)fe(factorize(m[i]),p,b)if(exponent_max_congruence[p].ba_mod_prime_pow,m_mod_prime_pow; fe(exponent_max_congruence,p,v){ T pq=pw(p,v.b); a_mod_prime_pow.eb(v.a%pq); m_mod_prime_pow.eb(pq); } return chinese_remainder_theorem_coprime(a_mod_prime_pow,m_mod_prime_pow,M); } bool is_quadratic_residue(ll a,ll p){ a=mod(a,p); if(a==0)return 1; if(p==2)return 1; return pw(a,(p-1)>>1,p)==1; } ll sqrt_mod_prime(ll a,ll p){ a=mod(a,p); if(a==0)return 0; if(p==2)return a; if(!is_quadratic_residue(a,p))return-1; ll S=0,Q=p-1; while(~Q&1)Q>>=1,++S; ll R=pw(a,(Q+1)>>1,p),T=pw(a,Q,p),M=S; ll z=1; while(is_quadratic_residue(z,p))++z; ll c=pw(z,Q,p); while(T!=1){ ll nxM=0,t=T; while(t!=1)++nxM,(t*=t)%=p; ll b=pw(c,pw2(S-nxM-1),p); (R*=b)%=p; (T*=(b*b)%p)%=p; } return min(R,p-R); } ll sqrt_mod_prime_pow(ll a,ll p,ll q){ a=mod(a,p); if(a==0)return 0; ll t1=sqrt_mod_prime(a,p); if(q==1||t1==0||t1==-1)return t1; if(p==2){ if(q==2){ if(a%4!=1)return-1; return 1; }else{ if(a%8!=1)return-1; ll tk=1; fo(k,3,q){ ll sk=(tk*tk-a)>>k; tk+=pw2(k-1)*mod(sk,2LL); } return tk; } }else{ ll tk=t1; ll pk=p; fo(k,1,q){ ll sk=(tk*tk-a)/pk; tk+=pk*mod(-sk*inv_mod(tk*2,p),p); pk*=p; } return tk; } } ll sqrt_mod(ll a,ll m){ a=mod(a,m); if(a==0)return 0; assert(a&1||m&1); if(gcd(a,m)>1)return-1; vecremainders,moduli; fe(factorize(m),p,q){ ll pq=pw(p,q); ll c=sqrt_mod_prime_pow(a,p,q); if(c==-1)return-1; remainders.eb(c%pq); moduli.eb(pq); } return chinese_remainder_theorem(remainders,moduli); } single_testcase void solve(){ LL(P,g); LL(Q); fo(Q){ LL(a,b,c); ll r=sqrt_mod((b*b-a*c*4)*inv_mod(a*a*4,P),P); if(r==-1){ pp(-1); }else if(r==0){ pp(mod(-b*inv_mod(a*2,P)+r,P)); }else{ ll x1=mod(-b*inv_mod(a*2,P)+r,P); ll x2=mod(-b*inv_mod(a*2,P)-r,P); pp(min(x1,x2),max(x1,x2)); } } }}