Difference Sets

Question

suppose we have a set $$P=\{p_1,p_2,...,p_K\}$$ where $$1\leq p_k\leq N , k=1,...,K \qquad \& \quad p_k \in \mathbb{N} $$ and $p_k$'s are distinct. We calculate the differences as: $$d=p_i-p_j\mod N,\quad i\ne j$$ Now let $a_d$ denote the number of occurrence of d (d = 1, 2, . . . , N − 1), then we have a set $$A=\{a_1,a_2,...,a_{N-1} \}$$ As you know given $P$ and $N$, it is easy to build $A$; Although given $A$ and $K$ there could be many $P$'s leading to $A$ or even no possible $P$ leading to $A$. I want to know, given $A$ and $K$, is there any algorithm just saying whether there is a $P$ leading to this $A$ or not ?