Count B‑smooth Numbers in an Interval

Given a positive integer \(B\), a natural number \(n\) is called B‑smooth if none of its prime factors exceed \(B\). Equivalently, \(n\) is B‑smooth if it can be represented as a product of positive integers each no greater than \(B\). Given a closed interval \([n, n+m]\), your task is to count the number of B‑smooth numbers within that interval.

inputFormat

The input consists of three space‐separated integers: \(n\), \(m\), and \(B\). The interval to be considered is \([n, n+m]\).

outputFormat

Output a single integer: the count of B‑smooth numbers in the interval \([n, n+m]\).

sample

1 10 5

9