#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__);i=i##stop;i-=i##step) #define fe(a,i,...) for(auto&&__VA_OPT__([)i __VA_OPT__(,__VA_ARGS__]):a) #define multiple_testcases void solve();}int main(){my::io();int T;std::cin>>T;while(T--)my::solve();}namespace my{ void io(){cin.tie(nullptr)->sync_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,auto...a){arrayr{0,0,1};ll I=0;((r[I++]=a),...);if(!s&&I==1)swap(r[0],r[1]);r[0]-=s;return r;} constexpr char nl=10; constexpr char sp=32; lll pw(lll x,ll n){assert(n>=0);lll r=1;while(n)n&1?r*=x:r,x*=x,n>>=1;return r;} 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;} templateostream&operator<<(ostream&o,const std::pair&p){return o<ostream&operator<<(ostream&o,const array&a){fo(i,n)o<ostream&operator<<(ostream&o,const unordered_map&m){fe(m,e)o<concept vectorial=is_base_of_v,V>; 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;} }; 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));} auto mod(auto a,auto m){return(a%=m)<0?a+m:a;} auto inv_mod(auto x,auto m){assert(gcd(x,m)==1);decltype(x)a=mod(x,m),b=m,u=1,v=0;while(b)swap(u-=a/b*v,v),swap(a-=a/b*b,b);return mod(u,m);} auto pow_mod(auto x,auto n,auto m){if(n<0)n=-n,x=inv_mod(x,m);decltype(x)r=1;while(n){if(n&1)(r*=x)%=m;(x*=x)%=m;n>>=1;}return r;} uint64_t kth_root_floor(uint64_t a,ll k){ if (k==1)return a; auto is_within=[&](uint32_t x){uint64_t t=1;fo(k)if(__builtin_mul_overflow(t,x,&t))return false;return t<=a;}; uint64_t r=0; of(i,sizeof(uint32_t)*CHAR_BIT)if(is_within(r|(1u<v{0,0};ll I=0;((v[I++]=a),...);auto[l,r]=v;if(I==1)swap(l,r);static ll t=495;t^=t<<7,t^=t>>9;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 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;} ll kth_root_mod_prime(ll a,ll k,ll P){ if(k==0)return(a==1?1:-1); if(a==0)return 0; if(P==2)return a; k=mod(k,P-1); ll g=gcd(k,P-1); if(pow_mod(a,(P-1)/g,P)!=1)return-1; ll c=inv_mod(k/g,(P-1)/g); a=pow_mod(a,c,P); (k*=c)%=P-1; auto pe_root=[&](ll c,ll p,ll e){ ll t=0; ll pt=1; ll s=P-1; while(s%p==0)++t,s/=p; ll v=1; while(pow_mod(v,(P-1)/p,P)==1)++v; ll pe=pw(p,e); ll u=inv_mod(-s,pe); ll z=pow_mod(c,(s*u+1)/pe,P); ll c_inv=inv_mod(c,P); while(1){ ll zpe=pow_mod(z,pe,P); ll zpe_c=mod((lll)zpe*c_inv,P); ll t_dash=0; while(pow_mod(zpe_c,pw(p,t_dash),P)!=1)++t_dash; if(t_dash==0)break; ll E=t-t_dash; ll vspE=pow_mod(v,s*pw(p,E-e),P); ll A=pow_mod(v,s*pw(p,t-1),P); ll B=pow_mod(inv_mod(zpe_c,P),pw(p,t_dash-1),P); ll R=sqrt_floor(p)+1; ll A_inv=inv_mod(A,P); unordered_mapdict; ll k=0; fo(i,R+1)dict[B*pow_mod(A_inv,R*i,P)]=i; fo(j,R)if(ll key=pow_mod(A,j,P);dict.contains(key))k=R*dict[key]+j; z=mod(z*pow_mod(vspE,k,P),P); } return z; }; fe(factorize(k),p,e)a=pe_root(a,p,e); return a; } multiple_testcases void solve(){ LL(P,k,a); pp(kth_root_mod_prime(a,k,P)); }}