Problem K
Lots of Land
Since Robert is new to the potato business, he has initially purchased $n$ different potato varieties to try out in the first year. He plans to divide his plot of land into $n$ parts of equal area and plant one of the varieties on each. To make it easier for him to work the fields with his tractor, each new piece of land should itself be a rectangle and have integer side lengths. Help Robert to find a suitable division of his field.
Input
The input consists of:
-
One line with three integers $\ell , w, n$ ($1 \le \ell ,w \le 100$, $1 \le n \le 26$), the length and width of Robert’s field and the number of potato varieties.
Output
If there is no solution, output impossible. Otherwise output $\ell $ lines, each with $w$ uppercase letters, describing a possible division of Robert’s field. There should be the same number of occurrences of each of the first $n$ letters of the English alphabet, and for each letter, its occurrences should form a single rectangular region. If there is more than one solution, any one of them will be accepted.
| Sample Input 1 | Sample Output 1 |
|---|---|
4 4 4 |
AAAA BBCC BBCC DDDD |
| Sample Input 2 | Sample Output 2 |
|---|---|
6 15 9 |
GGGGGBBBBBBBBBB GGGGGAAAAAAAAAA IIIIIIIIIIEEEEE FFFFFFFFFFEEEEE CCCCCDDDDDHHHHH CCCCCDDDDDHHHHH |
| Sample Input 3 | Sample Output 3 |
|---|---|
100 100 26 |
impossible |
