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 (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 standnext to a girl. How is it possible?
Help Bob by writing a program that solves the generalized task.
Input
The single line contains three integers n, x and y (2 ≤ n ≤ 100 000; 0 ≤ x, y ≤ 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 "Impossible".