Submit Solution(Code Jam Page)
### Problem

### Input

### Output

### Limits

#### Small dataset

#### Large dataset

### Sample

In Case #1, you can run to the left and catch all three quail at the
same time, 12 meters to the left of the starting position, which takes 3
seconds.

In Case #2, one optimal strategy is to run to the left until the second quail is caught at -2 m, which takes one second, and then run to the right in pursuit of the first quail, which you will catch at 6 m, taking four more seconds.

Oh no -- your **N** pet quail have all gotten loose! You are currently at position 0 on a line; the **i**th quail starts off at some nonzero integer (positive or negative) position **P _{i}** on that line, in meters, and will continuously run away from you at a constant integer speed of

What is the minimum number of seconds it will take you to catch all of the quail?

The first line of the input gives the number of test cases, **T**. **T** test cases follow. Each begins with one line with two space-separated integers **Y**, your speed, and **N**, the number of quail, and is followed by two more lines with **N** space-separated integers each. The first of these gives the positions **P _{i}** of the quail, and the second gives the speeds

For each test case, output one line containing "Case #x: y", where x is the test case number (starting from 1) and y is the minimum number of seconds needed to catch all the quail.

y will be considered correct if it is within an absolute or relative error of 10^{-6} of the correct answer. See the FAQ for an explanation of what that means, and what formats of real numbers we accept.

1 ≤ **T** ≤ 100.

2 ≤ **Y** ≤ 1000.

-10^{7} ≤ **P _{i}** ≤ 10

1 ≤

1 ≤ **N** ≤ 25.

1 ≤ **N** ≤ 500.

Input |
Output |

2 4 3 -3 -6 -9 3 2 1 2 2 1 -1 1 1 |
Case #1: 3.000000 Case #2: 5.000000 |

In Case #2, one optimal strategy is to run to the left until the second quail is caught at -2 m, which takes one second, and then run to the right in pursuit of the first quail, which you will catch at 6 m, taking four more seconds.