Sams Transformation

Sam likes transformations and is given a task of transforming one positive integer into an- other positive integer. In order to do so, he is given the starting integer, ending integer and a set S containing N positive integers. At each step, Sam can convert the current integer X to either $\phi(X)$ or $X^{2}$, provided that the new integer belongs to set S. $\phi(X)$ is the number of integers less