The following problem was given as an assingment in Introduction to algorithms course:

You are given n intervals on real line (integer coordinates) and you have to choose a subset M such that at most k intervals from this subset pairwise intersect (intersection at endpoints doesn't count). Weight w_i of the interval [s_i, e_i] is defined as e_i - s_i. The goal is to find a subset M with maximal sum of interval weights.

I am aware of a solution of a more general problem, where weights of an intervals can be arbitrary. But since this problem was presented at Introduction of algorithms course I guess there has to be a simpler solution for this more specific case.

Any hints would be very appreciated. :)