| 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. | |