Boys and Girls

Time limit2sMemory limit256 MB

Summary

Arrange n children in a circle with B/G so that exactly x stand next to a boy and exactly y next to a girl, output the lexicographically smallest.

Level: Easy2 of 10
Topics: Implementation, Brute force, String
Solved: No attempts yet

Problem

$n$ children stand in a circle. The neighbours of a child are the children standing directly beside that child in the circle. A child stands next to a boy if at least one of its neighbours is a boy, and stands next to a girl if at least one of its neighbours is a girl. When $n$ is 2, the two children are each other's only neighbour.

Find an arrangement in which exactly $x$ children stand next to a boy and exactly $y$ children stand next to a girl.

Input

The single line contains three integers $n$ , $x$ and $y$ separated by spaces ( $2 \le n \le 100000$ , $0 \le x, y \le n$ ).

Output

If no arrangement satisfies both counts, print Impossible.

Otherwise print one string of length $n$ . Write B for a boy and G for a girl, listing the children in the order you meet them while walking around the circle in one direction. Any child may be the starting one, so every rotation of an arrangement also satisfies the counts. If several strings satisfy the counts, print the lexicographically smallest one. In that comparison B comes before G.

Examples12

Example 1
Input
```
10 5 7
```
Expected output
```
BGBGBGBGGG
```
Example 2
Input
```
10 3 8
```
Expected output
```
Impossible
```
Example 3
Input
```
2 1 1
```
Expected output
```
BG
```
Example 4
Input
```
2 2 0
```
Expected output
```
BB
```
Example 5
Input
```
2 0 2
```
Expected output
```
GG
```
Example 6
Input
```
3 2 3
```
Expected output
```
BGG
```
Example 7
Input
```
7 7 0
```
Expected output
```
BBBBBBB
```
Example 8
Input
```
6 0 6
```
Expected output
```
GGGGGG
```
Example 9
Input
```
12 12 12
```
Expected output
```
BBGGBBGGBBGG
```
Example 10
Input
```
16 12 12
```
Expected output
```
BBBBBBGGBBGGGGGG
```
Example 11
Input
```
16 13 13
```
Expected output
```
BBBBBGGBBGGBGGGG
```
Example 12
Input
```
9 6 9
```
Expected output
```
BBGGBGGGG
```