// #define _GLIBCXX_DEBUG
#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,b) for(int i=0;i<b;i++)
#define rrep(i,b) for(int i=b-1;i>=0;i--)
#define rep1(i,b) for(int i=1;i<b;i++)
#define repx(i,x,b) for(int i=x;i<b;i++)
#define rrepx(i,x,b) for(int i=b-1;i>=x;i--)
#define fore(i,a) for(auto i:a)
#define fore1(i,a) for(auto &i:a)
#define rng(x) (x).begin(), (x).end()
#define rrng(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define fi first
#define se second
#define pcnt __builtin_popcountll

using namespace std;
using namespace atcoder;

using ll = long long;
using ld = long double;
template<typename T> using mpq = priority_queue<T, vector<T>, greater<T>>;
template<typename T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<typename T> bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<typename T> ll sumv(const vector<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;}
bool yn(bool a) { if(a) {cout << "Yes" << endl; return 1;} else {cout << "No" << endl; return 0;}}
#define dame { cout << "No" << endl; return 0;}
#define dame1 { cout << -1 << endl; return 0;}
#define test(x) cout << "test" << x << endl;
#define deb(x,y) cout << x << " " << y << endl;
#define debp(p) cout << p.fi << " " << p.se << endl;
#define deb3(x,y,z) cout << x << " " << y << " " << z << endl;
#define deb4(x,y,z,x2) cout << x << " " << y << " " << z << " " << x2 << endl;
#define out cout << ans << endl;
#define outd cout << fixed << setprecision(20) << ans << endl;
#define outm cout << ans.val() << endl;
#define outv fore(yans , ans) cout << yans << "\n";
#define outdv fore(yans , ans) cout << yans.val() << "\n";
#define show(x) cerr<<#x<<" = "<<x<<endl;
#define showdeb(x,y) cerr<<#x<<" = "<<x<<" : "<<#y<<" = "<<y<<endl;
#define showv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}
#define showv2(v) fore(vy , v) cout << vy << "\n";
#define showvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define showvm2(v) fore(vy , v) cout << vy.val() << "\n";
using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;using pii = pair<int,int>;using pdd = pair<ld,ld>;
using tp = tuple<int ,int ,int>;
using vi = vector<int>;using vd = vector<ld>;using vl = vector<ll>;using vs = vector<string>;using vb = vector<bool>;
using vpii = vector<pii>;using vpli = vector<pli>;using vpll = vector<pll>;using vpil = vector<pil>;
using vvi = vector<vector<int>>;using vvl = vector<vector<ll>>;using vvs = vector<vector<string>>;using vvb = vector<vector<bool>>;
using vvpii = vector<vector<pii>>;using vvpli = vector<vector<pli>>;using vvpll = vector<vpll>;using vvpil = vector<vpil>;
using mint = modint998244353;
using vm = vector<mint>;
using vvm = vector<vector<mint>>;
vector<int> dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1};
ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;}
ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}
#define yes {cout <<"Yes"<<endl;}
#define yesr { cout <<"Yes"<<endl; return 0;}
#define no {cout <<"No"<<endl;}
#define nor { cout <<"No"<<endl; return 0;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;

int main(){
    int t; cin>>t;

    vl ans(t);

    rep(i,t){
        ll p,q,k; cin>>p>>q>>k;

        ll d = gcd(p,q);
        p /= d;
        q /= d;

        ll mid = p*q;

        ll rr = mid % q;
        ll hi = mid / q;
        hi++;
        ll tmp = floor_sum(hi,p,q,rr);
        tmp += hi-1;

        if (tmp < k){
            ans[i] = p*q + (k-tmp);
            ans[i] *= d;
            continue;
        }

        auto check = [&](ll mid)->bool{
            ll rr = mid % q;
            ll hi = mid / q;
            hi++;

            ll tmp = floor_sum(hi,p,q,rr);

            tmp += hi-1;

            return tmp >= k;
        };


        ll l = 0,r=p*q+1;

        while(r - l > 1){
            ll mid = (l+r) / 2;

            if (check(mid)) r = mid;
            else l = mid;
        }

        ans[i] = r * d;
    }

    outv;

// 消せ！！！！！！　#define _GLIBCXX_DEBUG
// priority_queue でしぬ

    return 0;
}