FIICode 2024 Open | The Best Farm

Erniv and Kaimao, the prominent farmers of the Summoner's Rift, often find themselves at odds. In an effort to mend their relationship, King Kong-Wu offers them a piece of land from his kingdom to work on together. This land is a rectangle with a length of $l$ meters and a width of $w$ meters. Both Erniv and Kaimao reluctantly agree to work together and decide to divide the land into $n$ equal sections. They aim to make this division easier by ensuring that each new piece of land remains a rectangle, with side lengths being integers. Can you assist them in finding a suitable way to divide their field?

Input

One line with three integers $l$, $w$, and $n$ ($1 \le l, w, n \le 500$), representing the length and width of Kong-Wu's field and the number of divisions that Erniv and Kaimao decided to do.

Output

If there is no solution, display impossible. Otherwise, display possible and another $l$ lines, each containing $w$ numbers separated with a space between them, describing a possible division of Kong-Wu's field. The number of occurrences of each of the first $n$ numbers must be equal, and, for each number, its occurrences must form a single rectangular region. If there are multiple solutions, any of them is acceptable.

Example 1

stdin

4 4 4

stdout

possible
1 1 2 2 
1 1 2 2 
3 3 3 3 
4 4 4 4 

Example 2

stdin

100 100 33

stdout

impossible