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

def calc1(p,q,n):
  x=(q*n)//p
  return (x+1)*n-floor_sum(x+1,q,p,0)

def calc2(p,q,n,m):
  ng,ok=q,0
  while abs(ok-ng)>1:
    mid=(ok+ng)//2
    if floor_sum(n,q,p,q-mid)-floor_sum(n,q,p,0)>=n+1-m:
      ok=mid
    else:
      ng=mid
  return ok

import math

def solve(p,q,k):
  g=math.gcd(p,q)
  p,q=min(p,q)//g,max(p,q)//g
  m=q*(p-1)-(p-1)*(q-1)//2
  if k>m:
    res=k-m-1+q*(p-1)
    return res*g

  ng,ok=0,p+1
  while abs(ok-ng)>1:
    mid=(ok+ng)//2
    if k<=calc1(p,q,mid):
      ok=mid
    else:
      ng=mid
  
  if ok==0:
    x=k
  else:
    x=k-calc1(p,q,ok-1)
  
  return (q*(ok-1)+calc2(p,q,(ok*q)//p+1,x))*g

t=int(input())
for _ in range(t):
  p,q,k=map(int,input().split())
  print(solve(p,q,k+1))