from math import gcd
def floor_sum(n,m,a,b):
  ans=0
  while True:
    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
    n,m,a,b=y_max,a,m,(a-x_max%a)%a
T = int(input())
for _ in range(T):
    P,Q,K=map(int,input().split())
    ok = 10 ** 18
    ng = 0
    def isok(z):
        r = z//P
        if floor_sum(r+1,Q,P,Q+z-P*r)-1>= K:
            return True
        else:
            return False
    while ok -ng > 1:
        z = (ok+ng)>>1
        if isok(z):
            ok = z
        else:
            ng = z
    print(ok)