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Задачі

Co-prime

Co-prime

Ліміт часу 1 секунда
Ліміт використання пам'яті 64 MiB

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.

Вхідні дані

The first line on input contains T (0 < T100) the number of test cases, each of the next T lines contains three integers A, B, N where (1AB10^15) and (1N10^9).

Вихідні дані

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.

Приклад

Вхідні дані #1
2
1 10 2
3 15 5
Вихідні дані #1
Case #1: 5
Case #2: 10
Джерело The Third Lebanese Collegiate Programming Contest