P7032 [NWRRC 2016] Boys and Girls

Bob found a nice task in his old math book for children. It says: There are $10$ children standing in a circle, $5$ of them stand next to a boy, and $7$ of them stand next to a girl. How is it possible? Here is the solution to the task. If $4$ boys and $6$ girls stand like this: BGBGBGBGGG, there are $5$ children who stand next to a boy (here they are underlined: BGBGBGBGGG), and $7$ children who stand next to a girl $(BGBGBGBGGG).$ Now Bob wants to solve a generalized version of this task: There are $n$ children standing in a circle, $x$ of them stand next to a boy, and $y$ of them stand next to a girl. How is it possible? Help Bob by writing a program that solves the generalized task.

The single line of the input contains three integers $n , x$ and $y (2 \le n \le 100 000$ ; $0 \le x , y \le n)$ .

If there is a solution, output a string of length $n$ , describing the order of children in the circle. $Character ‘G'$ corresponds to a girl, character $‘B'$ corresponds to a boy. If there are several solutions, output any $of the_m.$ If there is no solution, output `Impossible`.

Time limit: 2 s, Memory limit: 256 MB.