#include<iostream>
#include<utility>
using namespace std;
long long floor_sum(long long N,long long M,long long A,long long B)
//Sum[floor((A*i+B)/M),{i,0,N-1}]
{
	long long ans=0;
	if(B>=M)
	{
		ans+=N*(B/M);
		B%=M;
	}
	while(true)
	{
		ans+=N*(N-1)/2*(A/M);
		A%=M;
		long long Ym=(A*N+B)/M,Xm=Ym*M-B;
		if(Ym==0)return ans;
		long long TX=(Xm+A-1)/A;
		ans+=(N-TX)*Ym;
		N=Ym;
		B=TX*A-Xm;
		swap(A,M);
	}
}
int gcd(int a,int b)
{
	while(b)
	{
		int t=a%b;
		a=b;
		b=t;
	}
	return a;
}
long long count(long long X,int P,int Q)
//Sum[floor((X-Pi+Q)/Q),{i,0,Q-1}]
{
	long long R=min((long long)Q,X/P+1);
	return floor_sum(R,Q,P,X+Q-P*(R-1));
}
int main()
{
	int T;
	cin>>T;
	for(;T--;)
	{
		int P,Q,K;
		cin>>P>>Q>>K;
		int g=gcd(P,Q);
		P/=g;
		Q/=g;
		long long l=0,r=(long long)P*Q+K;
		while(r-l>1)
		{
			long long mid=(l+r)/2;
			if(count(mid,P,Q)<=K)l=mid;
			else r=mid;
		}
		cout<<r*g<<endl;
	}
}