#include <bits/stdc++.h>
using namespace std;

__int128_t safemod(__int128_t a,__int128_t m){
    a %= m; a += m;
    return a>=m?a-m:a;
}
__int128_t floor(__int128_t a,__int128_t b){
    if(b < 0) a *= -1,b *= -1;
    return a<0?(a+1)/b-1:a/b; 
}
__int128_t ceil(__int128_t a,__int128_t b){
    if(b < 0) a *= -1,b *= -1;
    return a>0?(a-1)/b+1:a/b; 
}
__int128_t floorsum(__int128_t N,__int128_t M,__int128_t a,__int128_t b){
    //return Σ(i=0~N-1)floor((a*i+b)/M).
    __int128_t ret = 0;
    if(a >= M) ret += a/M*(N*(N-1)/2),a %= M;
    if(b >= M) ret += b/M*N,b %= M;
    __int128_t maxy = a*N+b;
    if(maxy >= M) ret += floorsum(maxy/M,a,M,maxy%M);
    return ret;
}
long long floorsum2(__int128_t N,__int128_t M,__int128_t a,__int128_t b){
    if(N <= 0) return 0;
    __int128_t ret = 0;
    if(a < 0 || a >= M) ret += floor(a,M)*(N*(N-1)/2),a = safemod(a,M);
    if(b < 0 || b >= M) ret += floor(b,M)*N,b = safemod(b,M);
    __int128_t maxy = a*N+b;
    if(maxy >= M) ret += floorsum(maxy/M,a,M,maxy%M);
    return ret;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int T; cin >> T;
    while(T--){
        long long P,Q,K; cin >> P >> Q >> K;
        long long g = gcd(P,Q); P /= g,Q /= g;
        long long low = 0,high = 1e18;
        while(high-low > 1){
            long long mid = (high+low)/2;
            long long now = floorsum2(min(Q,mid/P+1),Q,-P,mid)+min(Q,mid/P+1);
            if(now >= K+1) high = mid;
            else low = mid;
        }
        cout << high*g << "\n";
    }    
}