| What's the best thing about working at Facebook? It's hard to say, but the |
| free food doesn't hurt. Every day there are long lines for food, and sometimes |
| guests visit the campus, as hungry as everybody else. It pays to be a good |
| host, so sometimes we'll let guests cut ahead in the line. But obviously |
| nobody wants to miss out on delicious Facebook food. |
|
|
| Every day, **N** Facebook employees are lined up for lunch, and every day |
| **M** visitors come to the campus looking for food. Each person has an |
| appetite **Ai**, which is a positive integer. Curiously, no two people have |
| the same appetite. |
|
|
| If people with large appetites eat first, there's a concern that the food |
| might run out before the people at the back get to eat, so it's ideal to have |
| people with smaller appetites further ahead in the line. With this in mind, |
| we'd like to squeeze all of the guests into the lunch line as efficiently as |
| possible. |
|
|
| We define the _unsuitableness_ of a line as the number of pairs of people in |
| the line, **Pi** and **Pj**, such that **Pi** is ahead of **Pj** in the line, |
| and **Pi** has a larger appetite than **Pj**. Your task is to find a way to |
| get all the visitors into the lunch line such that the unsuitableness of the |
| resulting line is minimized. The employees that are standing in line won't |
| change order, but you can put guests in any place you want. |
|
|
| ### Input |
|
|
| The first line contains an integer **T**, the number of test cases. |
| Each test case has three lines: |
| A line with **N** and **M**. |
| A line with **N** integers, the appetites of the employees in order, beginning |
| with the first employee. |
| A line with **M** integers, the appetites of the visitors. |
|
|
| ### Output |
|
|
| For each test case _i_, output "Case #i: " followed by the minimum possible |
| unsuitableness of the resulting line. |
|
|
| ### Constraints |
|
|
| 1 ≤ **T** ≤ 20 |
| 1 ≤ **N** ≤ 105 |
| 1 ≤ **M** ≤ 105 |
| 1 ≤ **Ai** ≤ 109 |
|
|
| ### Explanation of Sample |
|
|
| For the first test case the optimal lunch line has the following appetites in |
| order: 1, 2, 3, 4 |
| For the second test case the optimal lunch line is: 1, 2, 4, 7, 5, 3 |
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|
