Jealous Numbers

There is a trouble in Numberland, prime number $p$ is jealous of another prime number $q$. She thinks that there are more integer numbers between $a$ and $b$, inclusively, that are divisible by greater power of $q$ than that of $p$. Help $p$ to get rid of her feelings.

Let \alpha(n, x) be maximal $k$ such that $n$ is divisible by x^k. Let us say that a number $n$ is $p$-dominating over $q$ if \alpha(n, p) > \alpha(n, q). Find out for how many numbers between $a$ and $b$, inclusive are $p$-dominating over $q$.