Migrated from Lutece 833 How Long Do You Have to Draw

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Description

There are two horizontal lines on the $XoY$ plane. One is $y_1 = a$, the other is $y_2 = b$($a < b$). On line $y_1$, there are $N$ points from left to right, the x-coordinate of which are $x = c_1, c_2, \cdots c_N$ ($c_1 < c_2 < \cdots < c_N$) respectively. And there are also $M$ points on line $y_2$ from left to right. The x-coordinate of the $M$ points are $x = d_1, d_2, \cdots d_M$ ($d_1 < d_2 < \cdots < d_M$) respectively.

Now you can draw segments between the points on $y_1$ and $y_2$ by some segments. Each segment should exactly connect one point on $y_1$ with one point on $y_2$.

The segments cannot cross with each other. By doing so, these segments, along with $y_1$ and $y_2$, 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?

Input

The first line has a number $T$ ($T \leq 20$) , indicating the number of test cases.

For each test case, first line has two numbers $a$ and $b$ ($0 \leq a$, $b \leq 10^4$), which is the position of $y_1$ and $y_2$.

The second line has two numbers $N$ and $M$ ($1 \leq N$, $M \leq 10^5$), which is the number of points on $y_1$ and $y_2$.

The third line has $N$ numbers $c_1, c_2, \cdots , c_N$($0 \leq c_i < c_{i+1} \leq 10^6$), which is the $x$-coordinate of the $N$ points on line $y_1$.

The fourth line has $M$ numbers $d_1, d_2, \cdots , d_M$($0 \leq d_i < d_{i+1} \leq 10^6$), which is the $x$-coordinate of the $M$ points on line $y_2$.

Output

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.

Samples

1
0 1
2 3
1 3
0 2 4

Case #1: 5.66

Resources

2013 ACM-ICPC China Chengdu Provincial Programming Contest