Clique Boolean Expression

Chef Ada constructed a simple undirected graph $G$ with $N$ vertices (numbered $1$ through $N$) as follows: * Start with a [complete graph](https://en.wikipedia.org/wiki/Complete_graph) with $K$ vertices and $K \cdot (K-1)/2$ edges. * Then, add $N-K$ vertices one by one. After adding each vetex, find some [clique](https://en.wikipedia.org/wiki/Clique_(graph_theory)) of $K-1$ vertices in the graph