There are $n$ spheres in 3D-space, labeled by $1,2,\dots,n$. The $i$-th sphere's center is at $(x_i,y_i,z_i)$, and the radius of it is $r_i$.
Let's denote the distance between the $i$-th sphere and the $j$-th sphere $d(i,j)$ as
\[d(i,j)=\max(0,\sqrt{(x_i-x_j)^2+(y_i-y_j)^2+(z_i-z_j)^2}-r_i-r_j)\]
That means choosing two points $P$ and $Q$, where $P$ is on the $i$-th sphere's surface or inside it, $Q$ is on the $j$-th sphere's surface or inside it, and minimize the Euclidean distance bewteen $P$ and $Q$.
There are $\frac{n(n-1)}{2}$ pairs of $i,j(1\leq i<j\leq n)$, please find the $k$-th smallest values among these $d(i,j)$.