#include<iostream>
using namespace std;


long long f(long long n, long long a, long long b) {
    return a * n + b;
}

long long floorSum(long long n, long long m, long long a, long long b) {
    if (n == 0) return 0;

    long long toAdd = (a / m) * n * (n - 1) / 2 + (b / m) * n;

    a %= m;
    b %= m;

    return toAdd + f(n - 1, a, b) / m + floorSum(f(n - 1, a, b) / m, a, m, f(n - 1, a, b) % m);
}


int P, Q, K;

void read() {
    cin >> P >> Q >> K;
}


int gcd(int a, int b) {
    if (b == 0) return a;
    return gcd(b, a % b);
}


void work() {
    int div = gcd(P, Q);
    P /= div;
    Q /= div;

    long long LT = 0, GE = 1LL * P * Q - 1;
    while (LT + 1 < GE) {
        long long mid = (LT + GE) / 2;

        if (floorSum(mid / P + 1, Q, P, mid - (mid / P) * P) + mid / P < K) {
            LT = mid;
        } else {
            GE = mid;
        }
    }

    if (GE == 1LL * P * Q - 1) {
        long long toAdd = K - (floorSum(GE / P + 1, Q, P, GE - (GE / P) * P) + GE / P);
        cout << (GE + toAdd) * div << endl;
    } else {
        cout << GE * div << endl;
    }
}


int main() {
    int T;
    cin >> T;
    for (int i = 0; i < T; ++i) {
        read();
        work();
    }
    return 0;
}