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

# https://github.com/shakayami/ACL-for-python/blob/master/math.py
# \sum_{i=0}^{n-1} (a * i + b)//m
def floor_sum(n,m,a,b):
    ans=0
    if a<0:
        a2=a%m
        return floor_sum(n,m,a2,b)-n*(n-1)*((a2-a)//m)//2
    if b<0:
        b2=b%m
        return floor_sum(n,m,a,b2)-n*((b2-b)//m)
    if a>=m:
        ans+=(n-1)*n*(a//m)//2
        a%=m
    if b>=m:
        ans+=n*(b//m)
        b%=m
    y_max=(a*n+b)//m
    x_max=(y_max*m-b)
    if y_max==0:
        return ans
    ans+=(n-(x_max+a-1)//a)*y_max
    ans+=floor_sum(y_max,a,m,(a-x_max%a)%a)
    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)