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