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## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Goal

You like to solve Minesweeper levels ? You will love generating them !

How to generate a level

* A level is a width x height cells grid. Its origin is the top left corner. It contains n mines.
* The level is generated only when the player selects the first cell. The 3x3 cells square centered on this cell is always set free of mines.
* To generate a mine, X and Y grid coordinates (X first and then Y) are randomly generated until an available position is found. To generate X (resp. Y), use the random value modulo width (resp. height).

Controlling randomness

The random number generator used to generate the level is a pseudo random number generator (PRNG) initialized with a seed provided in the inputs. The PRNG works as follows:

The nth generated value is:
R(n) = (214013 * R(n-1) + 2531011) / 65536
with R(0) = seed
R(1) is the first value to use.

With a seed of 31, the expected five first values produced by the PRNG are 139, 492, 1645, 5410, 17705.

You must use a single instance of PRNG for the whole generation. All calculations must be in 32-bit unsigned numbers. Beware that some languages (Python for instance) implicitly generate big integers without overflowing.
Input
A single line: width the level width, height the level height, n the number of mines for the level, x, y the coordinates of the first selected cell, seed the seed for the random number generator
Output
height lines: for each line, a row of cells starting from the top row. Each cell is represented by a single ASCII code without space between chars.

Cell format

* # for a cell containing a mine
* . for a cell without any mines next to it
* otherwise 1-8 for the number of neighboring cells containing mines
Constraints
5 ≤ width ≤ 30
5 ≤ height ≤ 16
5 ≤ n ≤ 99
Example
Input
`6 6 7 3 3 31`
Output
```1#2##1
222221
#1..11
331.1#
##1.11
221...```

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