Adamma is a climate scientist interested in temperature. Every minute,
she records the current temperature as an integer, creating a long list
of integers: _{1}, x_{2}, ..., x_{N}

This morning, she decided to compute a sliding average of this list in
order to get a smoother plot. She used a smoothing window of size **K**, which means that she converted the sequence of **N** temperatures into a sequence of **N** - **K** + 1)_{1}, s_{2}, ..., s_{N-K+1}._{i} is the average of the values _{i}, x_{i+1}, ..., x_{i+K-1}._{i} values were all integers, but some of the s_{i} may be fractional.

Unfortunately, Adamma forgot to save the original sequence of
temperatures! And now she wants to answer a different question -- what
was the difference between the largest temperature and the smallest
temperature? In other words, she needs to compute _{1}, ..., x_{N}} - min{x_{1}, ..., x_{N}}.**N**, **K**, and the smoothed sequence.

After some thinking, Adamma has realized that this might be impossible
because there may be several valid answers. In that case, she wants to
know the smallest possible answer among all of the possible original
sequences that could have produced her smoothed sequence with the given
values of **N** and **K**.

The first line of the input gives the number of test cases, **T**. **T** test cases follow; each test case consists of two lines. The first line contains integers **N** and **K** separated by a space character. The second line contains integer values _{1}, sum_{2}, ..., sum_{N-K+1},_{i} is given by _{i} / **K**

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 smallest possible difference between the largest and smallest temperature.

1 ≤ **T** ≤ 100.

2 ≤ **K** ≤ **N**.

The sum_{i} will be integers between -10000 and 10000, inclusive.

2 ≤ **N** ≤ 100.

2 ≤ **N** ≤ 1000.

2 ≤ **K** ≤ 100.

Input |
Output |

3 10 2 1 2 3 4 5 6 7 8 9 100 100 -100 7 3 0 12 0 12 0 |
Case #1: 5 Case #2: 0 Case #3: 12 |

0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5

The integer sequence that gives the smallest difference is:

0, 1, 1, 2, 2, 3, 3, 4, 4, 5

Note that the sequence:

0.5, 0.5, 1.5, 1.5, 2.5, 2.5, 3.5, 3.5, 4.5, 4.5

Would give the same smoothed sequence with a maximum difference of 4, but this is not a valid answer because the original temperatures are known to have been integers.

In Case #2, all we know is that the sum of the 100 original values was -100. It's possible that all of the original values were exactly -1, in which case the difference between the largest and smallest temperatures would be 0, which is as small as differences get!

In Case #3, the original sequence could have been:

-4, 8, -4, 8, -4, 8, -4

Points | Correct | Attempted |
---|---|---|

6pt | 194 | 268 |

7pt | 184 | 194 |