You are given an undirected graph of ~N~ vertices and ~M~ edges. Compute the number of subsets of vertices which are cliques, where the vertices not in the subset form an independent set.
~1 \le N, M \le 2 \cdot 10^5~
The first line contains two space-separated integers, ~N~ and ~M~.
Each of the next ~M~ lines contain two space-separated integers, ~a~ and ~b~, indicating an edge between ~a~ and ~b~. The input is guaranteed to contain no self-loops or parallel edges.
Count the number of valid subsets modulo ~10^9 + 7~.
3 3 1 2 1 3 2 3