hackercupai/hackercup huggingface dataset:
It is a truth universally acknowledged that a grandparent in possession of a
good fortune must furnish his or her grandchildren with cash on their
birthdays. Your usual approach is to give each of your **N** grandchildren a
number of dollars equal to their age, (That means 0 dollars for newborns; it's
important that they learn what a rough place the world is from the very
start).

One of your younger, and more precocious, grandchildren, Elly, has read online
that trying out new things is a good way to prevent Alzheimer's. So, out of
concern for your mental well-being (and in the hopes that she might receive
more money), she's posed a new distribution scheme. "If any two grandchildren
compare the size of their presents, they should find that both presents are
divisible by an integer **K**. They should also find that there is no larger
integer that divides the size of both presents," she states.

Well, that seems harmless enough, you think. Of course, each grandchild will
still have to receive at least as much money as they would have under the old
scheme, to avoid any family drama. As you're getting on in years, your
mathematical prowess isn't what it used to be. It would be easier to write a
program that computes the additional drain on your pocketbook.

Note that 0 is divisible by all other numbers.

### Input

The first line of the input consists of a single integer **T**, the number of
test cases.
Each test case starts with a line with the integers **N** and **K**.
The next line consists of the ages of your grandchildren as **N** integers
**A1**, **A2**, ..., **AN**.

### Output

For each test case **i** numbered from 1 to **T**, output "Case #**i**: ",
followed by the minimum extra amount of money you would have to spend compared
to giving everyone money equal to their age.

### Constraints

1 ≤ **T** ≤ 20
2 ≤ **N** ≤ 20
1 ≤ **K** ≤ 20
0 ≤ **Ai** ≤ 50

### Examples

In the first example, you would have to pay 2 to one of them and 3 to the
other. The total cost would be 5. Under the old constraints, both
grandchildren would get 2, for a total sum of 4. The answer is 5-4 = 1. You
can't pay 2 to both, because their gifts would be divisible by 2 as well as 1.

In the second example, a possible solution is to give them 3, 7, 5 and 16
dollars, for a total of 31. Under the old constraints, you would give them a
total of 28. The answer is 31-28 = 3.

In the third example, all gifts have to be divisible by 3. A possible solution
is 6, 21, 51. This is 6 more than the sum of their ages. Note that 6, 18, 51
are all divisible by 3, but 6 and 18 are both divisible by 6 as well, so that
solution is not valid.