import sys
input = sys.stdin.readline
from math import gcd

# https://qiita.com/AkariLuminous/items/3e2c80baa6d5e6f3abe9
# \sum_{i=0}^{n-1} (a * i + b)//m
def floor_sum(n, m, a, b):
    ans = 0
    while True:
        if a >= m or a < 0:
            ans += n * (n - 1) * (a // m) // 2
            a %= m
        if b >= m or b < 0:
            ans += n * (b // m)
            b %= m
        y_max = a * n + b
        if y_max < m: break
        n, b, m, a = y_max // m, y_max % m, a, m
    return ans

def BinarySearch(yes, no, P, Q, K):
    while abs(yes - no) != 1:
        mid = (yes + no)//2
        num = min(P, mid//Q + 1)
        if floor_sum(num, P, -Q, mid) + num - 1 >= K:
            yes = mid
        else:
            no = mid
    return yes


T = int(input())
for _ in range(T):
    P, Q, K = map(int, input().split())
    g = gcd(P, Q)
    P //= g
    Q //= g
    yes = 10 ** 20
    no = -1
    print(BinarySearch(yes, no, P, Q, K) * g)