#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <queue>
#include <set>
using namespace std;
typedef long long ll;
#define rep(i, n) for(int i = 0; i < (n); i++)
#define dump(x) cout << #x << " = " << (x) << endl;

template<class T>
using vi = vector<T>;

template<class T>
using vii = vector<vi<T>>;

template<class T>
using viii = vector<vii<T>>;

template<class T>
T floor_sum(T n, T m, T a, T b) { //sigma(i=0~n-1){[(ai+b)/m]}
    T res = 0;
    res += (a / m) * n * (n - 1) / 2;
    res += (b / m) * n;
    a = a % m;
    b = b % m;
    T ymax = a * n + b;
    if (ymax < m) return res;
    res += floor_sum(ymax / m, a, m, ymax % m);
    return res;
}

ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }

int main()
{
    int t;
    cin >> t;
    //ACL
    /*
    while (t--) {
        int n, m, a, b;
        cin >> n >> m >> a >> b;
        ll ans = floor_sum<ll>(n, m, a, b); 
        cout << ans << endl;
    }*/

    //yukicoder 2066
    while (t--) {
        ll p, q, k;
        cin >> p >> q >> k;
        ll g = gcd(p, q);
        p /= g;
        q /= g;
        ll ok = 0, ng = min(p, q) * k + 1;
        while (ng - ok > 1) {
            ll mid = (ok + ng) / 2;
            ll cnt = min(mid / q, p - 1);
            ll n = mid / q + 1;
            ll m = p;
            ll a = q;
            ll b = mid % q;
            cnt += floor_sum<ll>(n, m, a, b);
            if (n >= p) cnt -= floor_sum<ll>(n - p, m, a, b);
            if (cnt < k) ok = mid;
            else ng = mid;
        }
        cout << ng * g << endl;
    }
    return 0;
}


// https://atcoder.jp/contests/practice2/tasks/practice2_c