Palindromic Game Problem Code: PALINGAM

There are two players A, B playing a game. Player A has a string s with him, and player B has string t with him. Both s and t consist only of lower case English letters and are of equal length. A makes the first move, then B, then A, and so on alternatively. Before the start of the game, the players know the content of both the strings s and t.

These players are building one other string w during the game. Initially, the string w is empty. In each move, a player removes any one character from their respective string and adds this character anywhere (at any position) in the string w. If at any stage of the game, the string w is of length greater than 1 and is a palindrome, then the player who made the last move wins.

If even after the game finishes (ie. when both s and t have become empty strings), no one is able to make the string w a palindrome, then player B wins.

Given the strings s, and t, find out which of A, B will win the game, if both play optimally.

Input

• The first line of the input contains an integer T, corresponding to the number of test cases. The description of each testcase follows.
• The first line of each testcase will contain the string s.
• The second line of each testcase will contain the string t.

Output

For each test case, output "A" or "B" (without quotes) corresponding to the situation, in a new line.

Constraints

• Subtask 1 (20 points) : 1 ≤ T ≤ 500, All characters of string s are equal, All characters of string t are equal. 1 ≤ |s| = |t| ≤ 500
• Subtask 2 (80 points) : 1 ≤ T ≤ 500, 1 ≤ |s| = |t| ≤ 500

Example

Input:
3
ab
ab
aba
cde
ab
cd
Output:
B
A
B

Explanation

Testcase 1: If A adds ‘a‘ to w in the first move, B can add ‘a‘ and make the string w = "aa",

which is a palindrome,and hence win. S

imilarly, you can show that no matter what A plays, B can win.Hence the answer is B.

Testcase 2: Player A moves with ‘a‘, player B can put any of the character ‘c‘, ‘d‘ or ‘e‘, Now Player A can create a palindrome by adding ‘a‘.

Testcase 3: None of the players will be able to make a palindrome of length > 1. So B will win.

—————————————————————————————————————————————

這道題就是有兩個人A和B 他們每個人有一個串

（A先起手）每次一個人人能拿出自己串中剩余的字母中的一個加入現有串C的左邊或者右邊

當C變成一個回文串的時候遊戲結束 使這個串變成回文串的一方勝利

我們考慮A起手 如果他下了一個B有的字母 那麽無疑B會勝利

如果他下了一個B沒有的字母 且這個字母他有兩個 那麽他一定勝利

不然 如果B下的這個字母A有那麽A會勝利 不然不論如何下這個串都不會成為回文串

那麽平局下 按提議B會勝利

codechef AUG17 T4 Palindromic Game