/*
#include<kyopro/master>
namespace my{entry
void main(){
  multi_test_cases
  LL(a,b,K);K++;
  ll g=gcd(a,b);
  a/=g,b/=g;
  
  ll N=binary_search_first_true(1,oo,[&](ll N){
    ll L=min(b,N/a+1);
    return floor_sum(L,b,-a,N)+L>=K;
  });
  
  pp(N*g);
}}*/

#include<bits/stdc++.h>
#if __has_include(<atcoder/all>)
#endif
using namespace std;
#define RD(T,...) T __VA_ARGS__;lin(__VA_ARGS__)
#define LL(...) RD(ll,__VA_ARGS__)
#define FO(n) for(ll IJK=n;IJK-->0;)
#define defpp template<ostream&o=cout>void pp(const auto&...a){[[maybe_unused]]const char*c="";((o<<c<<a,c=" "),...);o<<'\n';}void epp(const auto&...a){pp<cerr>(a...);}
#define entry defpp void main();void main2();}int main(){my::io();my::main();}namespace my{
#define multi_test_cases LL(T);FO(T)main2();}void main2(){
namespace my{
void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<<fixed<<setprecision(15);}
using ll=long long;
using lll=__int128_t;
void lin(auto&...a){(cin>>...>>a);}
constexpr auto abs(auto x){return x<0?-x:x;}
constexpr ll size10(auto x){x|=1;ll r=0;while(x>0)x/=10,++r;return r;}
template<class T>constexpr ll maxsize10(){return size10(numeric_limits<T>::max());}
auto min(auto...a){return min(initializer_list<common_type_t<decltype(a)...>>{a...});}
template<class T,class U>common_type_t<T,U>gcd(T a,U b){return b?gcd(b,a%b):abs(a);}
ll binary_search_first_true(ll l,ll r,auto&&f){while(l+1<r)(f((l+r)/2)?r:l)=(l+r)/2;return r;}
template<bool is_negative=false>struct infinity{
  template<integral T>static constexpr T ones(size_t n){return n?ones<T>(n-1)*10+1:0;}
  template<integral T>constexpr operator T()const{return ones<T>(maxsize10<T>())*(1-is_negative*2);}
};
constexpr infinity oo;
}
namespace my{
template<class T=lll>T floor_sum(lll n,lll m,lll a,lll b){
  if(n<=0)return 0;
  if(a<0)return-floor_sum<T>(n,m,-a,-b+m-1);
  if(b<0)return floor_sum<T>(n,m,a,b*(1-m))+(T)b*n;
  if(a>=m||b>=m)return floor_sum<T>(n,m,a%m,b%m)+(T)(n-1)*n/2*(a/m)+(T)n*(b/m);

  if(a==0)return 0;
  return floor_sum<T>((a*n+b)/m,a,m,(a*n+b)%m);
}
}
namespace my{entry
void main(){
  multi_test_cases
  LL(a,b,K);K++;
  ll g=gcd(a,b);
  a/=g,b/=g;

  ll N=binary_search_first_true(1,oo,[&](ll N){
    ll L=min(b,N/a+1);
    return floor_sum(L,b,-a,N)+L>=K;
  });

  pp(N*g);
}}