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 fikaraster1.

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.

-----Examples-----
Sample Input:
4 4
10 3 3
Sample Output:
impossible

Source: kattis | Difficulty: HARD


Solutions: