P13389 [GCJ 2010 Qualification] Theme Park

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!

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. $g_{0}$ is the size of the first group, $g_{1}$ is the size of the second group, etc.

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.

**Sample Explanation** - $1 \leqslant T \leqslant 50.$ - $g_{i} \leqslant k.$ **Small dataset (10 Pts, Test set 1 - Visible)** - $1 \leqslant R \leqslant 1000.$ - $1 \leqslant k \leqslant 100.$ - $1 \leqslant N \leqslant 10.$ - $1 \leqslant g_{i} \leqslant 10.$ **Large dataset (23 Pts, Test set 2 - Hidden)** - $1 \leqslant R \leqslant 10^{8}.$ - $1 \leqslant k \leqslant 10^{9}.$ - $1 \leqslant N \leqslant 1000.$ - $1 \leqslant g_{i} \leqslant 10^{7}.$