B - Boys and Girls

Time limit: 2 s
Memory limit: 256 MiB
Languages: C, C++, Java, Tiger, ... (details)

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.

Input

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

Output

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 them. If there is no solution, output $\texttt{Impossible}$.

Sample test(s)

Input
10 5 7
Output
BGBGBGBGGG
Input
10 3 8
Output
Impossible