How Long Do You Have to Draw

There are two horizontal lines on the XoY plane. One is y₁ = a, the other is y₂ = b(a < b). On line y₁, there are N points from left to right, the x-coordinate of which are x = c₁, c₂, ... , c_N (c₁ < c₂ < ... < c_N) respectively. And there are also M points on line y₂ from left to right. The x-coordinate of the M points are x = d₁, d₂, ... d_M (d₁ < d₂ < ... < d_M) respectively.
Now you can draw segments between the points on y₁ and y₂ by some segments. Each segment should exactly connect one point on y₁ with one point on y₂.
The segments cannot cross with each other. By doing so, these segments, along with y1 and y2, can form some triangles, which have positive areas and have no segments inside them.
The problem is, to get as much triangles as possible, what is the minimum sum of the length of these segments you draw?

The first line has a number T (T <= 20) , indicating the number of test cases.
For each test case, first line has two numbers a and b (0 <= a, b <= 10⁴), which is the position of y₁ and y₂.
The second line has two numbers N and M (1 <= N, M <= 10⁵), which is the number of points on y₁ and y₂.
The third line has N numbers c₁, c₂, .... , c_N(0 <= c_i < c_i+1 <= 10⁶), which is the x-coordinate of the N points on line y₁.
The fourth line has M numbers d₁, d₂, ... , d_M(0 <= d_i < d_i+1 <= 10⁶), which is the x-coordinate of the M points on line y₂.

For test case X, output "Case #X: " first, then output one number, rounded to 0.01, as the minimum total length of the segments you draw.

1
0 1
2 3
1 3
0 2 4

Case #1: 5.66

2013 ACM/ICPC Asia Regional Online —— Warmup2