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.

Constraints

~1 \le N, M \le 2 \cdot 10^5~

Input Specification

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.

Output Specification

Count the number of valid subsets modulo ~10^9 + 7~.

Sample Input

3 3
1 2
1 3
2 3

Sample Output

4