Co-prime

Given a number N, you are asked to count the number of integers between A and B inclusive which are relatively prime to N.
Two integers are said to be co-prime or relatively prime if they have no common positive divisors other than 1 or, equivalently, if their greatest common divisor is 1. The number 1 is relatively prime to every integer.

The first line on input contains T (0 < T <= 100) the number of test cases, each of the next T lines contains three integers A, B, N where (1 <= A <= B <= 10¹⁵) and (1 <=N <= 10⁹).

For each test case, print the number of integers between A and B inclusive which are relatively prime to N. Follow the output format below.

2
1 10 2
3 15 5

Case #1: 5
Case #2: 10

In the first test case, the five integers in range [1,10] which are relatively prime to 2 are {1,3,5,7,9}.

The Third Lebanese Collegiate Programming Contest