hidden subgroup problem

=this.problem-name

Let $f$ be a function from a finitely generated group $G$ to a finite set $X$ such that $f$ is constant on the cosets of a subgroup $K$, and distinct on each coset. Given aquantum black box for performing the unitary transform $U |g|h = |g|h⊕f (g)$,for $g ∈ G$, $h ∈ X$, and $⊕$ an appropriately chosen binary operation on $X$, find agenerating set for $K$.