P8887 [DMOI-R1] Corgi Chess.

Little A and Little B are both dog lovers and extremely smart. They especially love corgis, so they invented “Corgi Chess”.

Little A and Little B take turns making moves on an $n \times n$ chessboard. Little A moves first, and Little B moves second. Suppose a “corgi” is placed at $(x,y)$. Then the four positions $(x-1,y-1)$, $(x-1,y+1)$, $(x+1,y-1)$, and $(x+1,y+1)$ on the board will all become this corgi’s territory, meaning no other “corgi” can be placed there. If a player cannot place a “corgi” anymore, then that player loses. Unfortunately, Little C does not really like corgis, so he strongly opposes Little A and Little B playing “Corgi” chess, and he likes to mess up their game. When Little A and Little B have placed a total of $x_i$ “corgis”, Little C will expand the current $w \times w$ board into a $(w+2) \times (w+2)$ board, centered at the center of the current $w \times w$ board. He will interfere a total of $q$ times. Your task is to determine whether Little A wins or Little B wins. If Little A wins, output `A won`; otherwise, output `B won`. Since they are quite playful, they will play a total of $T$ games. **Note**: 1. When Little A and Little B have already played on the original board until no more moves can be made, they will directly jump to Little C’s next interference (if any). 2. Little A and Little B know that Little C will interfere, and they will play according to their optimal strategies. Due to the data being too large, $x_i$ is given by a random data generator.

The first line contains a positive integer $T$, indicating there are $T$ test cases. Each test case contains one line with three positive integers $n,q,seed$, where the purpose of $seed$ is explained in the hint.

Output $T$ lines. Each line should be the string `A won` or `B won`.

### Random Data Generator In each game, $x_i$ is generated by the following generator: ```cpp unsigned long long x[10000005]; unsigned long long xor_shift(unsigned long long &seed){ return seed^=seed>>12, seed^=seed27, seed*0x2545F4914F6CDD1D; } int main(){ //your code here int n,q; unsigned long long seed; cin>>n>>q>>seed; for(int i=1;i