Problem

Roller coasters are so much fun! It seems like everybody who visits the theme park wants to ride the roller coaster. Some people go alone; other people go in groups, and don't want to board the roller coaster unless they can all go together. And everyone who rides the roller coaster wants to ride again. A ride costs 1 Euro per person; your job is to figure out how much money the roller coaster will make today.

The roller coaster can hold k people at once. People queue for it in groups. Groups board the roller coaster, one at a time, until there are no more groups left or there is no room for the next group; then the roller coaster goes, whether it's full or not. Once the ride is over, all of its passengers re-queue in the same order. The roller coaster will run R times in a day.

For example, suppose R=4, k=6, and there are four groups of people with sizes: 1, 4, 2, 1. The first time the roller coaster goes, the first two groups [1, 4] will ride, leaving an empty seat (the group of 2 won't fit, and the group of 1 can't go ahead of them). Then they'll go to the back of the queue, which now looks like 2, 1, 1, 4. The second time, the coaster will hold 4 people: [2, 1, 1]. Now the queue looks like 4, 2, 1, 1. The third time, it will hold 6 people: [4, 2]. Now the queue looks like [1, 1, 4, 2]. Finally, it will hold 6 people: [1, 1, 4]. The roller coaster has made a total of 21 Euros!

Input

The first line of the input gives the number of test cases, T. T test cases follow, with each test case consisting of two lines. The first line contains three space-separated integers: R, k and N. The second line contains N space-separated integers g_i, each of which is the size of a group that wants to ride. g₀ is the size of the first group, g₁ is the size of the second group, etc.

Output

For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is the number of Euros made by the roller coaster.

Limits

Time limit: 30 1 second(s) per test set.

Memory limit: 1GB.

1 ≤ T ≤ 50.

g_i ≤ k.

Small dataset (Test set 1 - Visible; 10 Points)

1 ≤ R ≤ 1000.

1 ≤ k ≤ 100.

1 ≤ N ≤ 10.

1 ≤ g_i ≤ 10.

Large dataset (Test set 2 - Hidden; 23 Points)

1 ≤ R ≤ 10⁸.

1 ≤ k ≤ 10⁹.

1 ≤ N ≤ 1000.

1 ≤ g_i ≤ 10⁷.

Sample

3
4 6 4
1 4 2 1
100 10 1
1
5 5 10
2 4 2 3 4 2 1 2 1 3

Case #1: 21
Case #2: 100
Case #3: 20