Flipping coins

Alice and Bob are playing a game , everyone has a string made of 0/1, Alice's one called A , and Bob's one called B.
There is an uniform coin and an empty string $S$. When the game start, every round they toss the coin , if the coin face up, add a '0' to the bottom of $S$, otherwise add a '1'.
At the end of every round, they check if A or B becomes a substring of $S$, if A is the substring of $S$ , Alice wins, and if B is the substring of $S$ , Bob wins. In order to avoid the two person win at the same time. A will not be a suffix of B, and B will not be a suffix of A either.
Now we get A and B , we want to know whether the game is fair. if it's unfair , who will more going to be winner?

There is a number T shows there are T test cases below. ($T \leq 50$)
For each test case contains a line , including the string A and B.
$1 \leq |A|,|B| \leq 100$

For each case output, if the game is fair , output "Fair" , otherwise output "A" or "B" who has more chance to win.

2
0 1
011 110

Fair
A

BestCoder Round #28