B-Smooth Numbers

Let $B$ be a positive integer. A positive integer $x$ is called a $B$-smooth number if none of its prime factors is greater than $B$. Equivalently, $x$ is $B$-smooth when it can be written as a product of positive integers that are each at most $B$. (In particular, $1$ is $B$-smooth for every $B$.)

Given three positive integers $n$, $m$ and $B$, count how many $B$-smooth numbers lie in the closed interval $[n,\ n+m]$.

A single line contains three integers $n$, $m$ and $B$, separated by single spaces, where $1 \le n \le 2\,000\,000\,000$, $1 \le m \le 100\,000\,000$ and $1 \le B \le 1\,000\,000$.

Print a single integer: the number of $B$-smooth numbers in the interval $[n,\ n+m]$.