| At the arcade, you can play a simple game where a ball is dropped into the top | |
| of the game, from a position of your choosing. There are a number of pegs that | |
| the ball will bounce off of as it drops through the game. Whenever the ball | |
| hits a peg, it will bounce to the left with probability 0.5 and to the right | |
| with probability 0.5. The one exception to this is when it hits a peg on the | |
| far left or right side, in which case it always bounces towards the middle. | |
| When the game was first made, the pegs where arranged in a regular grid. | |
| However, it's an old game, and now some of the pegs are missing. Your goal in | |
| the game is to get the ball to fall out of the bottom of the game in a | |
| specific location. Your task is, given the arrangement of the game, to | |
| determine the optimal place to drop the ball, such that the probability of | |
| getting it to this specific location is maximized. | |
| The image below shows an example of a game with five rows of five columns. | |
| Notice that the top row has five pegs, the next row has four pegs, the next | |
| five, and so on. With five columns, there are four choices to drop the ball | |
| into (indexed from 0). Note that in this example, there are three pegs | |
| missing. The top row is row 0, and the leftmost peg is column 0, so the | |
| coordinates of the missing pegs are (1,1), (2,1) and (3,2). In this example, | |
| the best place to drop the ball is on the far left, in column 0, which gives a | |
| 50% chance that it will end in the goal. | |
| x.x.x.x.x | |
| x...x.x | |
| x...x.x.x | |
| x.x...x | |
| x.x.x.x.x | |
| G | |
| 'x' indicates a peg, '.' indicates empty space. | |
| ### Input | |
| You should first read an integer **N**, the number of test cases. Each of the | |
| next **N** lines will then contain a single test case. Each test case will | |
| start with integers **R** and **C**, the number of rows and columns (**R** | |
| will be odd). Next, an integer **K** will specify the target column. Finally, | |
| an integer **M** will be followed by **M** pairs of integer **ri** and **ci**, | |
| giving the locations of the missing pegs. | |
| ### Constraints | |
| * 1 ≤ **N** ≤ 100 | |
| * 3 ≤ **R**,**C** ≤ 100 | |
| * The top and bottom rows will not have any missing pegs. | |
| * Other parameters will all be valid, given **R** and **C** | |
| ### Output | |
| For each test case, you should output an integer, the location to drop the | |
| ball into, followed by the probability that the ball will end in columns | |
| **K**, formatted with exactly six digits after the decimal point (round the | |
| last digit, don't truncate). | |
| ### Notes | |
| The input will be designed such that minor rounding errors will not impact the | |
| output (i.e. there will be no ties or near -- up to 1E-9 -- ties, and the | |
| direction of rounding for the output will not be impacted by small errors). | |