Problem

You are given a prime number $p$ and a range of integers. Your task is to count how many integers in the range are primitive roots modulo $p$.

An integer $g$ is called a primitive root modulo $p$ if its powers generate all non-zero residues modulo $p$.

In other words, the values $g^1 \bmod p,\ g^2 \bmod p,\ \dots,\ g^{p-1} \bmod p$ contain every number from $1$to$p-1$ exactly once.

Return the count of numbers in the given interval that satisfy this property.