Every set of powers of a prime occurs as the set of degrees of irreducible representations of a class two group

Statement
Suppose $$p$$ is a prime number. Suppose $$S$$ is any finite set all of whose elements are powers of $$p$$ and such that $$1 \in S$$. Then, there exists a group of nilpotency class two $$G$$ that is also a finite p-group such that the degrees of irreducible representations of $$G$$ over a splitting field (such as $$\mathbb{C}$$) comprise precisely the elements of $$S$$. (Note that the degrees of irreducible representations information also includes the number of times each degree appears, so this information is lost when we pass to $$S$$).