# Bonbons

Ylva loves bonbons, probably more than anything else on this
planet. She loves them so much that she made a large plate of
$R \cdot C$ bonbons for
her *fikaraster*^{1}.

Ylva has a large wooden tray which can fit $R$ rows of $C$ bonbons per row, that she will put
the bonbons on. Her bonbons have three different fillings:
Nutella Buttercream, Red Wine Chocolate Ganache, and Strawberry
Whipped Cream. Since Ylva is a master chocolatier, she knows
that presentation is $90\%
$ of the execution. In particular, it looks very bad if
two bonbons of the same color are adjacent to each other within
a row or a column on the tray. We call an arrangement of
bonbons where this is never the case a *good
arrangement*.

Given the number of bonbons of each flavour, and the size of Ylva’s tray, can you help her find a good arrangement of the bonbons, or determine that no such arrangement exists?

## Input

The first line of input contains the two space-separated integers $2 \le R, C \le 1000$. The next line contains three non-negative space-separated integers $a, b, c$ – the number of bonbons of the three flavours which Ylva has baked. It is guaranteed that $a + b + c = R \cdot C$. Both $R$ and $C$ will be even.

## Output

If no good arrangement can be found, output `impossible`. Otherwise, output $R$ lines, each containing
$C$ characters,
representing a good arrangement. Each row should contain only
characters `A, B, C`, depending on
which flavour should be placed on a certain position. The
number of `A` bonbons placed must be
equal to $A$, and so
on.

Sample Input 1 | Sample Output 1 |
---|---|

4 4 10 3 3 |
impossible |

Sample Input 2 | Sample Output 2 |
---|---|

4 4 6 5 5 |
ABCA BCAB CABC ABCA |

**Footnotes**

- “Fikarast” is a Swedish word, meaning to take a break from work while enjoying coffee and pastries together with your colleagues.