A Population of Rabbits

A hypothetical population of rabbits follows fixed rules.

1. In the first month the population is one pair of newborn rabbits.
2. A pair can mate starting the month after it is born.
3. Every pair that can mate does so, in every month.
4. A pair that mates gives birth to one male and one female, a new pair, in the next month.
5. A pair lives until the month its age reaches $D$ months, and it stops breeding once its age passes $R$ months, where $R \le D$.

An age is 1 month in the month a pair is born and grows by 1 each month. So a pair born in month $b$ is alive in months $b$ through $b + D - 1$, and it mates in every month where its age is at least 2 and at most $R$, that is in months $b + 1$ through $b + R - 1$.

Take $D = 3$ and $R = 3$. A pair lives three months and mates twice. The first pair is born in month 1, mates in month 2, and its first child pair is born in month 3. That same pair mates again in month 3, so a second child pair is born in month 4. The first pair dies in month 4, so it is not counted in the population of month 4.

Given $D$, $R$ and $M$, write a program that counts the rabbit pairs alive in month $M$.

The first line contains the number of test cases $N$ ($1 \le N \le 100$). Each of the next $N$ lines contains three positive integers $D$, $R$, $M$. Here $D$ is the age at which a pair dies, $R$ is the age after which a pair stops breeding, and $M$ is the month whose population you report. The bounds are $D \le 100$, $R \le 100$, $M \le 20$ and $R \le D$.

For each test case print one line of the form Case #n: k, where $n$ is the test case number starting at 1 and $k$ is the number of rabbit pairs alive in month $M$.