Digital Scoreboard

Arkady Semyonovich Tapkin has an electronic clock in his room. The digits on this clock are shown in a special pseudographic style. Each cell in which a digit is drawn is $w$ cells wide and $h$ cells high, and the cells in the field are squares.

But recently Arkady Semyonovich has had a problem. Lately his eyesight has gotten worse. For this reason he wants to enlarge the image of these digits. He has already connected an old $19"$ monitor to the clock, and now the only thing left is to write a program that will draw the digits on the display. Arkady Semyonovich wants to enlarge the image by a factor of $k$ and make the line thickness equal to $d$. Help him with this.

Let us describe the notion of <<enlarging by a factor of $k$>> more formally. Number the cells of the $w \times h$ field from top to bottom and from left to right. Thus the upper left cell has coordinates $(0, 0)$, the lower right cell is $(w - 1, h - 1)$, the upper right cell is $(w - 1, 0)$, and the lower left cell is $(0, h - 1)$. In addition, introduce a Cartesian rectangular coordinate system such that the origin is at the center of the upper left cell, the $Ox$ axis points to the right, the $Oy$ axis points down, and the length of the unit segment is equal to the side length of a cell. Thus the coordinates of the center of a cell coincide with its coordinates in the numbering introduced above.

Each decimal digit is given by a set of segments that make up its image. For simplicity, each segment is either parallel to one of the coordinate axes or at a 45-degree angle to it.

The digit enlarged by a factor of $k$ is drawn on a field of $(w - 1) \cdot (k - 1) + w$ cells horizontally by $(h - 1) \cdot (k - 1) + h$ cells vertically.

When a digit is enlarged by a factor of $k$, the following operations are performed. The coordinates of the points that are the endpoints of the segments making up the digit are multiplied by $k$. After that, the cells through whose centers these segments pass are painted. We call these cells main.

After that, to obtain a line thickness of $d$, the cells whose centers are at a distance not exceeding $(d - 1)$ from the centers of the main cells are painted additionally. The distance between points $A(x\_A, y\_A)$ and $B(x\_B, y\_B)$ is the number $\rho(A, B) = |x\_A - x\_B| + |y\_A - y\_B|$.

Given the description of a digit and the parameters $k$ and $d$, output the image of the digit enlarged by a factor of $k$ with line thickness $d$.

The first line of the input file contains the integers $k$ and $d$ ($1 \le k \le 100$, $1 \le d \le 500$). The second line of the input file contains the integers $w$ and $h$ ($1 \le w, h \le 10$).

The third line of the input file contains the integer $n$ ($1 \le n \le 100$), the number of segments in the description of the digit. This is followed by $n$ lines, each describing one segment. The description of a segment consists of four integers: $x\_1$, $y\_1$, $x\_2$, $y\_2$ ($0 \le x\_1, x\_2 < w$, $0 \le y\_1, y\_2 < h$), the coordinates of the endpoints of the segment.

Each segment is either parallel to one of the coordinate axes or at a 45-degree angle to it. All segments have nonzero length.

The output file must contain exactly $(h - 1) \cdot (k - 1) + h$ lines of $(w - 1) \cdot (k - 1) + w$ characters each. The $j$-th character of the $i$-th line must be the character <<*>> (asterisk) if the cell with center at $(j,i)$ is painted, and the character <<.>> (dot) otherwise.