[AtCoder ABC302] F - Merge Set
If we add edges between every pair of sets that have shared elements, there will be O(N^2) edges to traverse.
Instead, we can add N extra virtual vertices from 1 to N, each virtual node contains a single number.
Then we connect all sets to these N virtual vertices. There will be O(SUM of |SET|) edges, which is bounded by 5 * 10^5.
To find out the minimum steps to reach from 1 to M, we do a bfs and divide the min distance by 2 as the introduction of virtual nodes makes each 1 step hop to a 2 steps hop.
