Electronic Hunting
Since ancient times, hunting has been a part of human activity. Initially, it was a means to obtain food, but over time, it evolved into a form of entertainment, which has faced increasing opposition from animal rights advocates.
To find a middle ground between hunting enthusiasts and animal rights supporters, "electronic boar hunting" was created. This hunt takes place in a designated rectangular area divided into small squares, some of which are filled with dense shrubs, forming a "living" maze.
In one of the squares without shrubs, an electronic "boar" is released. This robot is programmed to take a specific number of steps. A step involves the "boar" moving from its current square to a neighboring square that is not filled with shrubs (horizontally, vertically, or diagonally), or it may choose to stay in place. The probability of the "boar" moving to any neighboring square or staying put is equal.
After the "boar" completes its set number of steps, the hunter, equipped with a laser rifle, selects a square without shrubs to shoot from. A shot is successful if the "boar" is visible from the chosen square, either vertically, horizontally, or diagonally, or if the boar is in the same square as the hunter. However, if there is a shrub-filled square between the hunter and the "boar" on the same line, the "boar" is considered invisible.
Your task is to help the hunter find the square with the highest probability of a successful shot.
Input
The first line contains two integers nX and nY, separated by a space, representing the horizontal and vertical size of the area, respectively (1 ≤ nX, nY ≤ 100).
The second line contains an integer K, the number of squares filled with shrubs (0 ≤ K < nX*nY).
The following K lines each contain two integers X and Y, indicating the coordinates of a square filled with shrubs (1 ≤ X ≤ nX, 1 ≤ Y ≤ nY). All pairs (X, Y) are guaranteed to be unique.
The last line contains three integers kX, kY, and N, separated by spaces, representing the initial coordinates of the "boar" and the number of steps it will take (1 ≤ kX ≤ nX, 1 ≤ kY ≤ nY, 1 ≤ N ≤ 50).
Output
The output should consist of two integers oX and oY, separated by a space, indicating the coordinates of the square with the highest probability of a successful shot. If multiple squares have the same probability, choose the one with the smallest X coordinate. If there is still a tie, choose the square with the smallest Y coordinate.
Two probability values are considered equal if their difference does not exceed 10^{‑6}.