Sonya and Segments

Sonya has $N$ segments on the $x$-axis. For each valid $i$, the $i$-th segment contains all points between $l_i$ and $r_i$ inclusive. Maks gave Sonya a magic number $K$. Sonya wants to choose exactly $K$ of her segments in such a way that the intersection of the chosen segments is empty, i.e. there is no point which is contained in each of the chosen segments. Find the number of ways in which Son