#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;

template <typename T>
T _gcd(const T &a, const T &b) {
    if (b == 0) return a;
    return _gcd(b, a % b);
}

template <typename T>
T _lcm(const T &a, const T &b) {
    return a * (b / _gcd(a, b));
}

// |x| と |y| は結果として max(a,b) 以下になる。
template <typename T>
T extgcd(const T &a, const T &b, T &x, T &y) {
    if (b == 0) {
        x = 1, y = 0;
        return a;
    }
    T g = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
    return g;
}

int mod(const long long &a, const int &m) {
    int ret = a % m;
    return ret + (ret < 0 ? m : 0);
}

// a と m は互いに素
int modinv(const int &a, const int &m) {
    int x, y;
    extgcd(a, m, x, y);
    return mod(x, m);
}

// Σ[0<=i<n] floor((ai+b)/m)
template <typename T>
T floor_sum(const T &n, const T &m, T a, T b) {
    T ret = (a / m) * (n * (n - 1) / 2) + (b / m) * n;
    a %= m, b %= m;
    T y = (a * n + b) / m;
    if (y == 0) return ret;
    ret += floor_sum(y, a, m, a * n - (m * y - b));
    return ret;
}

// min{ai+b mod m | 0<=i<n} またがないときコスト p, またぐときコスト q
template <typename T>
T linear_mod_min(T n, const T &m, T a, T b, bool is_min = true, T p = 1, T q = 1) {
    if (a == 0) return b;
    if (is_min) {
        if (b >= a) {
            T t = (m - b + a - 1) / a;
            T c = (t - 1) * p + q;
            if (n <= c) return b;
            n -= c;
            b += a * t - m;
        }
        b = a - 1 - b;
    } else {
        if (b < m - a) {
            T t = (m - b - 1) / a;
            T c = t * p;
            if (n <= c) return a * ((n - 1) / p) + b;
            n -= c;
            b += a * t;
        }
        b = m - 1 - b;
    }
    T d = m / a;
    T c = linear_mod_min(n, a, m % a, b, !is_min, (d - 1) * p + q, d * p + q);
    return is_min ? a - 1 - c : m - 1 - c;
}

template <typename T>
pair<T, T> Chinese_remainder_theorem(const T &a1, const T &m1, const T &a2, const T &m2) {
    T x, y, g = extgcd(m1, m2, x, y);
    if ((a2 - a1) % g != 0) return make_pair(0, -1);
    T m = m1 * (m2 / g);
    T tmp = mod(x * ((a2 - a1) / g), m2 / g);
    T a = (m1 * tmp + a1) % m;
    return make_pair(a, m);
}

// m の各要素がそれぞれ互いに素とは限らない場合の前処理
bool prepare_Garner(vector<int> &a, vector<int> &m) {
    int n = a.size();
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < i; j++) {
            int g = gcd(m[i], m[j]);
            if ((a[i] - a[j]) % g != 0) return false;
            m[i] /= g, m[j] /= g;
            int gi = gcd(m[i], g), gj = g / gi;
            do {
                g = gcd(gi, gj);
                gi *= g, gj /= g;
            } while (g > 1);
            m[i] *= gi, m[j] *= gj;
        }
    }
    return true;
}

// m の各要素はそれぞれ互いに素
int Garner(vector<int> a, vector<int> m, const int &M) {
    m.push_back(M);
    vector<long long> coeffs(m.size(), 1);
    vector<long long> constants(m.size(), 0);
    for (int k = 0; k < (int)a.size(); k++) {
        long long x = a[k] - constants[k], y = modinv(coeffs[k], m[k]);
        long long t = mod(x * y, m[k]);
        for (int i = k + 1; i < (int)m.size(); i++) {
            constants[i] += t * coeffs[i], constants[i] %= m[i];
            coeffs[i] *= m[k], coeffs[i] %= m[i];
        }
    }
    return constants.back();
}

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

    while (T--) {
        ll a, b, K;
        cin >> a >> b >> K;
        K++;

        ll g = gcd(a, b);
        a /= g, b /= g;

        ll L = 0, R = INF; // (L,R]
        while (R - L > 1) {
            ll M = (L + R) / 2;
            ll t = (M + b) / a;
            chmin(t, b - 1);
            ll tmp = floor_sum(t + 1, b, a, M + b - t * a);
            (tmp >= K ? R : L) = M;
        }

        cout << R * g << '\n';
    }
}