Cow Checkers

One day Bessie decides to challenge Farmer John to a game of "Cow Checkers". The game is played on an $M \times N$ checkerboard ($1 \le M \le 1{,}000{,}000$, $1 \le N \le 1{,}000{,}000$) that initially contains a single checker piece at coordinates $(X, Y)$ ($0 \le X < M$, $0 \le Y < N$). The bottom-left square of the board has coordinates $(0, 0)$, and the top-right square has coordinates $(M-1, N-1)$. Bessie always moves first, and then the two players alternate turns.

On each turn a player makes one of the following three moves:

1. Move the piece to any square in the same row that lies to the left of its current position.
2. Move the piece to any square in the same column that lies below its current position.
3. Move the piece to the square that is $k$ squares down and $k$ squares to the left of its current square, where $k$ is any positive integer for which the destination square is still on the board.

The first player who is unable to move (i.e., because the piece is at $(0, 0)$) loses. Given that Bessie always goes first and both players play optimally, determine who wins.

For $T$ games ($1 \le T \le 1{,}000$), read a new starting position $X, Y$ for each game and decide the winner.

• Line 1: Two space-separated integers $M$ and $N$
• Line 2: A single integer $T$
• Lines 3 through $T+2$: Two space-separated integers $X$ and $Y$ on each line

For each game print one line containing either Farmer John or Bessie, depending on who wins that game. Print $T$ lines in total.

Consider one game on a $3 \times 3$ checkerboard with the piece initially at $(1, 1)$ (the center of the board).

Bessie can initially move the piece only to $(1, 0)$, $(0, 1)$, or $(0, 0)$. Bessie can win immediately by moving the piece to $(0, 0)$.