Triangles on a Rectangle

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.

The first line of each testcase contains two integers $$$w$$$ and $$$h$$$ ($$$3 \le w, h \le 10^6$$$) — the coordinates of the corner of a rectangle.

The next two lines contain the description of the points on two horizontal sides. First, an integer $$$k$$$ ($$$2 \le k \le 2 \cdot 10^5$$$) — the number of points. Then, $$$k$$$ integers $$$x_1 < x_2 < \dots < x_k$$$ ($$$0 < x_i < w$$$) — the $$$x$$$ coordinates of the points in the ascending order. The $$$y$$$ coordinate for the first line is $$$0$$$ and for the second line is $$$h$$$.

The next two lines contain the description of the points on two vertical sides. First, an integer $$$k$$$ ($$$2 \le k \le 2 \cdot 10^5$$$) — the number of points. Then, $$$k$$$ integers $$$y_1 < y_2 < \dots < y_k$$$ ($$$0 < y_i < h$$$) — the $$$y$$$ coordinates of the points in the ascending order. The $$$x$$$ coordinate for the first line is $$$0$$$ and for the second line is $$$w$$$.

The total number of points on all sides in all testcases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

For each testcase print a single integer — the doubled maximum area of a triangle formed by such three points that exactly two of them belong to the same side.

Sample Input:

3
5 8
2 1 2
3 2 3 4
3 1 4 6
2 4 5
10 7
2 3 9
2 1 7
3 1 3 4
3 4 5 6
11 5
3 1 6 8
3 3 6 8
3 1 3 4
2 2 4

Sample Output:

25
42
35

Note:

The points in the first testcase of the example:

• $$$(1, 0)$$$, $$$(2, 0)$$$;
• $$$(2, 8)$$$, $$$(3, 8)$$$, $$$(4, 8)$$$;
• $$$(0, 1)$$$, $$$(0, 4)$$$, $$$(0, 6)$$$;
• $$$(5, 4)$$$, $$$(5, 5)$$$.

The largest triangle is formed by points $$$(0, 1)$$$, $$$(0, 6)$$$ and $$$(5, 4)$$$ — its area is $$$\frac{25}{2}$$$. Thus, the doubled area is $$$25$$$. Two points that are on the same side are: $$$(0, 1)$$$ and $$$(0, 6)$$$.