#include<bits/stdc++.h>
using namespace std;
int f(int a, int b){
    int count1=0;
    if(b==1) count1=a;
    else
      count1=f(a,b-1)*a;
    return count1;
}
int main(void){
    int a,b,n;
    int T;
    int count=0;
    int c,d;
    cin>>T;
    while(T && cin>>a>>b>>n)
    {
        T--;
        count=0;
       for(int i=1;count<n;i++)
       {
           c=a;
           d=b;
            if (f(a+1,b)<=f(a,b+1)) 
            {
              count=f(a+1,b);
              a=a+1;
            }
            else 
            {
             count=f(a,b+1);
             b=b+1;
            }
            if(count==f(c,d))
            {
             count=n;
             cout<<"A&B"<<endl;
            }
            else if(count>=n)
            {
             if(i%2)
               cout<<"A"<<endl;
             else
               cout<<"B"<<endl;
            }
        }
}        
}