2015/round1/homework.md

Your first-grade math teacher, Mr. Book, has just introduced you to an amazing
new concept — primes! According to your notes, a prime is a positive integer
greater than 1 that is divisible by only 1 and itself.

Primes seem fun, but without giving you and your 6-year-old colleagues time to
consider their implications, he's promptly gone on to define another term:
primacity. He explains that the primacity of an integer is the number of
distinct primes which divide it. For example, the primacity of 12 is 2 (as
it's divisible by primes 2 and 3), the primacity of 550 is 3 (as it's
divisible by primes 2, 5, and 11), and the primacity of 7 is 1 (as the only
prime it's divisible by is 7).

Following his lesson, Mr. Book has given you homework with some rather mean
questions of the following form: Given 3 integers **A**, **B**, and **K**, how
many integers in the inclusive range [**A**, **B**] have a primacity of
exactly **K**?

Mr. Book probably expects his little homework assignment to take you and your
classmates the rest of the year to complete, giving him time to slack off and
nap during the remaining math classes. However, you want to learn more things
from him instead! Can you use the skills you've learned in your first-grade
computer science classes to finish Mr. Book's homework before tomorrow's math
class?

### Input

Input begins with an integer **T**, the number of homework questions. For each
question, there is one line containing 3 space-separated integers: **A**,
**B**, and **K**.

### Output

For the **i**th question, print a line containing "Case #**i**: " followed by
the number of integers in the inclusive range [**A**, **B**] with a primacity
of **K**.

### Constraints

1 ≤ **T** ≤ 100  
2 ≤ **A** ≤ ** B** ≤ 107  
1 ≤ **K** ≤ 109  

### Explanation of Sample

In the first test case, the numbers in the inclusive range [5, 15] with
primacity 2 are 6, 10, 12, 14, and 15. All other numbers in this range have
primacity 1.