P11056 Fire and Big

Little F wants to play a game with others, but he does not want to lose, so he asks you to help him study a strategy. There are $m$ stones. Little F and Little B take turns removing stones. Little F goes first. The player who cannot make a move loses. Given a positive integer $n$, the number of stones removed each time $k$ ($k$ is a positive integer) must satisfy **at least one** of the following two conditions: - $k$ is a multiple of $n$. - $k$ is a perfect square less than $n$. They will play $T$ games. In each game, $n$ is fixed, and only the number of stones $m$ changes. For each game, assuming both players are smart enough, determine who has a winning strategy.

The first line contains two positive integers $T, n$. The second line contains $T$ positive integers $m$, where each $m$ is the number of stones in that game.

Output a string of length $T$, one character per game. Each character is `F` or `B`, meaning the first player wins or the second player wins in that game, respectively.

### Sample Explanation The following explains that when $n = 2, m = 3$, the second player will win. Consider the number of stones the first player removes on the first move: - If the first player removes $1$ stone, then the second player can remove all remaining $2$ stones. - If the first player removes $2$ stones, then the second player can remove the remaining $1$ stone. Therefore, no matter what, the second player will always win. ### Constraints | Test Point ID | $n$ | $m\le$ | | :----------: | :----------: | :----------: | | $1$ | $\le 5\times 10^5$ | $1$ | | $2\sim 3$ | $\le 5$ | $5$ | | $4\sim 6$ | $\le 10^5$ | $n$ | | $7\sim 8$ | $=2$ | $10^9$ | | $9\sim 11$ | $\le 5$ | $10^9$ | | $12\sim 14$ | $\le 10^3$ | $10^9$ | | $15\sim 17$ | $\le 10^5$ | $10^9$ | | $18\sim 20$ | $\le 5\times 10^5$ | $10^9$ | For all testdata, it is guaranteed that $1\le T, n\le 5\times 10^5$ and $1\le m\le 10^9$. **For odd-numbered test points, the memory limit is $512\ \text{MB}$; for even-numbered test points, the memory limit is $64\ \text{MB}$.** Translated by ChatGPT 5