atarw has bought a number of times table sets in preparation for the difficult math in the upcoming school year. A times table set is a rectangular collection of columns, with respective heights of a times table which somehow helps atarw to visualize the math.

Consider a 4 by 4 times table.

$${\displaystyle \begin{array}{ccccc}\times & 1& 2& 3& 4\\ 1& 1& 2& 3& 4\\ 2& 2& 4& 6& 8\\ 3& 3& 6& 9& 12\\ 4& 4& 8& 12& 16\end{array}}$$

These products are the heights of a set shown below.

1 2 3  4
2 4 6  8
3 6 9  12
4 8 12 16

He wants to stack them on top of each other $M$ times within an originally empty $C$ by $R$ grid to form a cool 3D structure. When stacked, gravity takes effect on the individual columns causing them to drop down. The grid has a top-left corner at $(1,1)$ and a bottom right corner at $(C,R)$. He may put more than one set at the same time. This effectively multiplies all the numbers (heights) in the times table.

2 4  6  8
4 8  12 16
6 12 18 24
8 16 24 32

After stacking these sets together, atarw wants to take a finger walk in the grid starting at position $(c,r)$. He wants to take the longest finger walk on a strictly increasing path. Output the largest sum of such a path. He may only finger walk to adjacent blocks (up, down, left, right).

Input Specification

The first line will contain three space separated integers, $CRM$, the number of columns and rows on the grid and the number of times that atarw will place multiplication table sets.

The next $M$ lines will contain 5 integers, x y w h n where $(x,y)$ is the top left corner of the multiplication table set(s). $w$ is the width and $h$ is the height of the set(s). $n$ is the number of sets to be inserted. It is guaranteed that the whole rectangle is within the grid.

Finally, the last line of input will contain c r, $(c,r)$ is the starting position of the finger walk. It is guaranteed that the coordinates are within the grid.

Constraints

Subtask 1 [20%]

$1\le C,R,M\le 100$
$1\le n\le 10$

Subtask 2 [80%]

$1\le C,R\le 500$
$1\le M\le 100000$
$1\le n\le 100$

Output Specification

A single integer, the largest sum of the longest finger walk possible modulo $1000000007$.

Sample Input 1

5 4 3
1 1 3 3 1
3 3 3 2 2
2 4 2 1 4
2 1

Sample Output 1

35

Explanation for Sample Output 1

The structure is:

1 2 3  0 0
2 4 6  0 0
3 6 11 4 6
0 4 12 8 12

The longest path is: $2\to 4\to 6\to 11\to 12$.

Sample Input 2

5 5 1
1 1 5 5 1
2 2

Sample Output 2

92