Chef and Circles

There are $N$ circles in a plane. Circle $i$ and circle $j$ form a *good pair* if it is possible to choose a point $P_1$ on the perimeter of circle $i$ and a point $P_2$ on the perimeter of circle $j$ such that the Euclidean distance between $P_1$ and $P_2$ is exactly $K$. (Note that $P_1$ and $P_2$ do not need to have integer coordinates.) You should answer $Q$ queries. In each query, you are