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MOG Training #2Ended |
B - Boys and Girls
Languages: C, C++, Java, Pascal, Haskell, Python, JavaScript, Tiger, C#
Time & Memory limits: (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