#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
template<int mod>istream &operator>>(istream &is,static_modint<mod> &a){long long b;is>>b;a=b;return is;}
istream &operator>>(istream &is,modint &a){long long b;cin>>b;a=b;return is;}
#endif
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}
#define reps(i,a,n) for(int i=(a);i<(n);i++)
#define rep(i,n) reps(i,0,n)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcount(x)
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T,size_t n,size_t id=0>
auto vec(const int (&d)[n],const T &init=T()){
  if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));
  else return init;
}
void SOLVE();
int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  #ifdef LOCAL
  clock_t start=clock();
  #endif
  int testcase=1;
  cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
  #ifdef LOCAL
  cerr<<"time:";
  cerr<<(clock()-start)/1000;
  cerr<<"ms\n";
  #endif
}
template<typename T>
T floorsum(T n,T m,T a,T b){
  assert(n>=0&&m>=1);
  T ret=0;
  if(a<0){
    T aa=a%m+m;
    ret-=n*(n-1)/2*((aa-a)/m);
    a=aa;
  }
  if(b<0){
    T bb=b%m+m;
    ret-=n*((bb-b)/m);
    b=bb;
  }
  while(true){
    if(a>=m){
      ret+=n*(n-1)/2*(a/m);
      a%=m;
    }
    if(b>=m){
      ret+=n*(b/m);
      b%=m;
    }
    T ymx=a*n+b;
    if(ymx<m)break;
    n=ymx/m;
    b=ymx%m;
    swap(m,a);
  }
  return ret;
}
void SOLVE(){
  ll p,q,k;
  cin>>p>>q>>k;
  ll g=gcd(p,q);
  p/=g,q/=g;
  ll ok=1e18,ng=0;
  while(ok-ng>1){
    ll mid=(ok+ng)/2;
    ll n=min(mid/p+1,q);
    if(floorsum<__int128_t>(n,q,p,mid-p*(n-1))+n-1>=k)ok=mid;
    else ng=mid;
  }
  cout<<ok*g<<endl;
}