Find the number of primitive roots modulo prime

Given a prime . The task is to count all the primitive roots of .
A primitive root is an integer x (1 <= x < p) such that none of the integers x - 1, x² - 1, ...., x^{p - 2} - 1 are divisible by but x^{p - 1} - 1 is divisible by . 
Examples: 
 

Input: P = 3 
Output: 1 
The only primitive root modulo 3 is 2. 
Input: P = 5 
Output: 2 
Primitive roots modulo 5 are 2 and 3. 
 

Approach: There is always at least one primitive root for all primes. So, using Eulers totient function we can say that f(p-1) is the required answer where f(n) is euler totient function.
Below is the implementation of the above approach: 
 

2

Time Complexity: O(p * log(min(a, b))), where a and b are two parameters of gcd.

Auxiliary Space: O(log(min(a, b)))