#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;
}
}
}
} 


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