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.

Input

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 ≤ 10^15) and (1 ≤ N ≤ 10^9).

Output

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.

Examples