Check if current interval is overlapping some intervals, or is being overlapped
Hint: Sort $\{l_1,r_1,\ldots,l_N,r_N\}$ and replace the sorted list with $1,\ldots,2N$ to effectively reduce $K$ to $2N$.

(There might be better ways of solving the problem, but this reduction at least gets rid of the dependence on $K$.)