#include #define pb push_back #define eb emplace_back #define fi first #define se second #define rep(i,N) for(long long i = 0; i < (long long)(N); i++) #define repr(i,N) for(long long i = (long long)(N) - 1; i >= 0; i--) #define rep1(i,N) for(long long i = 1; i <= (long long)(N) ; i++) #define repr1(i,N) for(long long i = (N) ; (long long)(i) > 0 ; i--) #define each(x,v) for(auto& x : v) #define all(v) (v).begin(),(v).end() #define sz(v) ((int)(v).size()) #define ini(...) int __VA_ARGS__; in(__VA_ARGS__) #define inl(...) long long __VA_ARGS__; in(__VA_ARGS__) #define ins(...) string __VA_ARGS__; in(__VA_ARGS__) using namespace std; void solve(); using ll = long long; template using V = vector; using vi = V; using vl = V<>; using vvi = V< V >; constexpr int inf = 1001001001; constexpr ll infLL = (1LL << 61) - 1; struct IoSetupNya {IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7);} } iosetupnya; template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template ostream& operator <<(ostream& os, const pair &p) { os << p.first << " " << p.second; return os; } template istream& operator >>(istream& is, pair &p) { is >> p.first >> p.second; return is; } template ostream& operator <<(ostream& os, const vector &v) { int s = (int)v.size(); rep(i,s) os << (i ? " " : "") << v[i]; return os; } template istream& operator >>(istream& is, vector &v) { for(auto &x : v) is >> x; return is; } void in(){} template void in(T &t,U &...u){ cin >> t; in(u...);} void out(){cout << "\n";} template void out(const T &t,const U &...u){ cout << t; if(sizeof...(u)) cout << " "; out(u...);} templatevoid die(T x){out(x); exit(0);} #ifdef NyaanDebug #include "NyaanDebug.h" #define trc(...) do { cerr << #__VA_ARGS__ << " = "; dbg_out(__VA_ARGS__);} while(0) #define trca(v,N) do { cerr << #v << " = "; array_out(v , N);cout << endl;} while(0) #else #define trc(...) #define trca(...) int main(){solve();} #endif #define in2(N,s,t) rep(i,N){in(s[i] , t[i]);} #define in3(N,s,t,u) rep(i,N){in(s[i] , t[i] , u[i]);} using vd = V; using vs = V; using vvl = V< V<> >; templateusing heap = priority_queue< T , V , greater >; using P = pair; using vp = V

; constexpr int MOD = /**/ 1000000007; //*/ 998244353; ////////////////// // 素数判定 O( sqrt(N) log log N ) // 0からNに対して素数->1、それ以外->0の配列を返す関数 vector Primes(int N){ vector A(N + 1 , 1); A[0] = A[1] = 0; for(int i = 2; i * i <= N ; i++) if(A[i]==1) for(int j = i << 1 ; j <= N; j += i) A[j] = 0; return A; } // 因数 O( sqrt(N) log log N ) // 0からNに対して素数->1、それ以外->最小の素数である因数、の配列を返す vector Factors(int N){ vector A(N + 1 , 1); A[0] = A[1] = 0; for(int i = 2; i * i <= N ; i++) if(A[i]==1) for(int j = i << 1 ; j <= N; j += i) A[j] = i; return A; } // オイラーのトーシェント関数 φ(N)=(Nと互いに素なN以下の自然数の個数) vector EulersTotientFunction(int N){ vector ret(N + 1 , 0); for(int i = 0; i <= N ; i++) ret[i] = i; for(int i = 2 ; i <= N ; i++){ if(ret[i] == i) for(int j = i; j <= N; j += i) ret[j] = ret[j] / i * (i - 1); } return ret; } // 約数列挙 O(sqrt(N)) // Nの約数を列挙した配列を返す vector Divisor(long long N){ vector v; for(long long i = 1; i * i <= N ; i++){ if(N % i == 0){ v.push_back(i); if(i * i != N) v.push_back(N / i); } } return v; } // 素因数分解 // 因数をkey、そのべきをvalueとするmapを返す // ex) N=12 -> m={ (2,2) , (3,1) } map PrimeFactors(long long N){ map m; for(long long i=2; i * i <= N; i++) while(N % i == 0) m[i]++ , N /= i; if(N != 1) m[N]++; return m; } // 原始根 modでrが原始根かどうかを調べる bool PrimitiveRoot(long long r , long long mod){ r %= mod; if(r == 0) return false; auto modpow = [](long long a,long long b,long long m)->long long{ a %= m; long long ret = 1; while(b){ if(b & 1) ret = a * ret % m; a = a * a % m; b >>= 1; } return ret; }; map m = PrimeFactors(mod - 1); each(x , m){ if(modpow(r , (mod - 1) / x.fi , mod ) == 1) return false; } return true; } // 拡張ユークリッド ax+by=gcd(a,b)の解 // 返り値 最大公約数 long long extgcd(long long a,long long b, long long &x, long long &y){ if(b == 0){ x = 1; y = 0; return a; } long long d = extgcd(b , a%b , y , x); y -= a / b * x; return d; } // ブール代数ライブラリ // Point. 乗法の単位元は-1 (UNIT & a = aを満たすUNITであるため) struct BA{ unsigned long long x; BA(): x(0){} BA(unsigned long long y):x(y){} BA operator += (const BA &p){ x = x ^ p.x; return (*this); } BA operator *= (const BA &p){ x = x & p.x; return (*this); } BA operator+(const BA &p)const {return BA(*this) += p;} BA operator*(const BA &p)const {return BA(*this) *= p;} bool operator==(const BA &p) const { return x == p.x; } bool operator!=(const BA &p) const { return x != p.x; } friend ostream &operator<<(ostream &os,const BA &p){ return os << p.x; } friend istream &operator>>(istream &is, BA &a){ unsigned int t; is >> t; a = BA(t); return (is); } }; int64_t mod_log(int64_t a, int64_t b, int64_t p) { int64_t g = 1; for(int64_t i = p; i; i /= 2) (g *= a) %= p; g = __gcd(g, p); int64_t t = 1, c = 0; for(; t % g; c++) { if(t == b) return c; (t *= a) %= p; } if(b % g) return -1; t /= g; b /= g; int64_t n = p / g, h = 0, gs = 1; for(; h * h < n; h++) (gs *= a) %= n; unordered_map< int64_t, int64_t > bs; for(int64_t s = 0, e = b; s < h; bs[e] = ++s) { (e *= a) %= n; } for(int64_t s = 0, e = t; s < n;) { (e *= gs) %= n; s += h; if(bs.count(e)) return c + s - bs[e]; } return -1; } // c++17での名前衝突を避けるためdefine #define gcd nyagcd #define lcm nyalcm ll nyagcd(ll x, ll y){ ll z; if(x > y) swap(x,y); while(x){ x = y % (z = x); y = z; } return y; } ll nyalcm(ll x,ll y){ return 1LL * x / gcd(x,y) * y; } void q(){ inl(p , k , a); // pの原始根 ll pr = 2; while(!PrimitiveRoot(pr , p)) pr++; trc(pr); ll l = mod_log(pr , a , p); trc(l); if(l == -1) {out(-1); return;} ll m , n; if(l % gcd(p - 1 , k) != 0){out(-1); return;} //if((p - 1) % gcd(l , k) != 0) {out(-1); return;} extgcd(k ,(p - 1) , n , m); n = n * l / gcd(p - 1 , k) % (p - 1); trc(n); if(n < 0) n = n % p - 1 , n += p - 1; ll ret = 1; while(n){ ret = ret * pr % (p - 1); pr = pr * pr % (p - 1); n >>= 1; } out(ret); } void solve(){ ini(T); rep(i,T) q(); }