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.

$$\displaystyle \begin{array}{c|cccc} \times & 1 & 2 & 3 & 4 \\\hline 1 & 1 & 2 & 3 & 4 \\ 2 & 2 & 4 & 6 & 8 \\ 3 & 3 & 6 & 9 & 12 \\ 4 & 4 & 8 & 12 & 16 \end{array}$$

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, ~C\ R\ M~, 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 100\,000~
~1 \le n \le 100~

Output Specification

A single integer, the largest sum of the longest finger walk possible modulo ~1\,000\,000\,007~.

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