#include using namespace std; #define rep(i,n) for(ll i=0;i=0;i--) #define perl(i,r,l) for(ll i=r-1;i>=l;i--) #define fi first #define se second #define pb push_back #define ins insert #define pqueue(x) priority_queue,greater> #define all(x) (x).begin(),(x).end() #define CST(x) cout<; using vvl=vector>; using pl=pair; using vpl=vector; using vvpl=vector; const ll MOD=1000000007; const ll MOD9=998244353; const int inf=1e9+10; const ll INF=4e18; const ll dy[8]={1,0,-1,0,1,1,-1,-1}; const ll dx[8]={0,1,0,-1,1,-1,1,-1}; template inline bool chmax(T &a, T b) { return ((a < b) ? (a = b, true) : (false)); } template inline bool chmin(T &a, T b) { return ((a > b) ? (a = b, true) : (false)); } //N=10^5,s<=10^10で1000msくらい struct fast_factorize{ using i128=__int128_t; vector wit={2, 325, 9375, 28178, 450775, 9780504, 1795265022}; ll modpow(ll a,ll b,ll m){ ll ret=1,now=a; while(b){ if(b&1)ret=i128(ret)*now%m; now=i128(now)*now%m; b>>=1; } return ret; } bool isprime(ll p){ if(p==2)return true; if(p==1||p%2==0)return false; ll s=0,d=p-1; while(d%2==0){ d/=2;s++; } for(auto a:wit){ if(a%p==0)continue; bool iscomp=true; ll x=modpow(a,d,p); if(x==1)iscomp=false; rep(i,s){ if(x==p-1)iscomp=false; x=i128(x)*x%p; } if(iscomp)return false; } return true; } long long find_factor(long long n) { assert(n > 1); if (n % 2 == 0) return 2; if (isprime(n)) return n; auto f = [&](__int128 x) -> long long { return (x * x + 1) % n; }; for (int t = 1;; t++) { long long x0 = t, m = max(n >> 3, 1LL), x, ys, y = x0, r = 1, g, q = 1; do { x = y; for (int i = r; i--;) y = f(y); long long k = 0; do { ys = y; for (int i = min(m, r - k); i--;) y = f(y), q = __int128(q) * abs(x - y) % n; g = gcd(q, n); k += m; } while (k < r and g <= 1); r <<= 1; } while (g <= 1); if (g == n) { do { ys = f(ys); g = gcd(abs(x - ys), n); } while (g <= 1); } if (g != n) return g; } } vector factor(ll n){ vector ret; while(n>1){ ll f=find_factor(n); if(f 0) { if (n & 1) res = res * a % mod; a = a * a % mod; n >>= 1; } return res; } random_device rd; mt19937 mt(rd()); ll primitive_root(ll n){ uniform_int_distribution<> rand(2,n-1); auto f=fz.factor(n-1); while(1){ ll r=rand(mt); bool ok=true; for(auto q:f){ if(modpow(r,(n-1)/q,n)==1)ok=false; } if(ok)return r; } } ll euler_phi(ll n) { ll ret = n; for(ll i = 2; i * i <= n; i++) { if(n % i == 0) { ret -= ret / i; while(n % i == 0) n /= i; } } if(n > 1) ret -= ret / n; return ret; } void solve(){ ll p,k,a;cin >> p >> k >> a; if(p==2){ cout << 1 << endl;return; } /*if(gcd(k,p-1)!=1){ cout << -1 << endl;return; }*/ ll e=0; ll r=primitive_root(p); { unordered_map mp; ll now=1; for(int i=0;i<8000;i++){ mp[now]=i; now=now*r%p; } ll ap=a; ll invnow=modpow(now,p-2,p); for(int i=0;i<125001;i++){ if(mp.count(ap)){ e=mp[ap]+i*8000;break; } ap=ap*invnow%p; } } //cout << r <<" " << e << endl; //if(modpow(r,e,p)!=a)cout <<"WA"<< endl; //x*k=e mod p-1 を求める ll x=INF; { unordered_map mp; ll now=0; for(int i=0;i<8000;i++){ mp[now]=i; now+=k; if(now>=p-1)now-=p-1; } ll ap=e%(p-1); for(int i=0;i<125001;i++){ if(mp.count(ap)){ x=i*8000+mp[ap]; break; } ap-=now; if(ap<0)ap+=p-1; } } //cout << x << endl; ll ans=modpow(r,x,p); if(modpow(ans,k,p)!=a)cout << -1 << endl; else cout << ans << endl; } int main(){ ios::sync_with_stdio(false); std::cin.tie(nullptr); ll t;cin >> t; while(t--){ solve(); } }