Exercise 5 (2 pts). The DENSE SUBGRAPH problem is defined as follows: . Input: (G, p, q) where G is a graph and p,q e Z . Question: Does G have p vertices such that there are at least q edges between them? Prove that this problem is NP-hard by giving a polynomial-time reduction of CLIQUE (known to be NP-hard) to DENSE SUBGRAPH. Hint. If a set of k vertices is a clique, how many edges are there between these k vertices