For a given set of K prime numbers S = {p1, p2, ..., pK}, consider the set of all numbers whose prime factors are a subset of S. This set contains, for example, p1, p1p2, p1p1, and p1p2p3 (among others). This is the set of `humble numbers' for the input set S. Note: The number 1 is explicitly declared not to be a humble number.
Your job is to find the Nth humble number for a given set S. Long integers (signed 32-bit) will be adequate for all solutions.