Zenny and Segments

$Zenny$ has a difficult problem to solve. She has $N$ segments $[l1,r1],[l2,r2],…,[lN,rN]$ on the x-axis. A $K$-subset of these $N$ segments consists of any $K$ of these segments. For each $K$-subset, consider the common intersection of all the $K$ segments, i.e. the set of points which belong to each of the $K$ segments. The intersection of segments is also a segment; the length of a segment $[l,