Eulerian Subgraphs

You are given an undirected graph that has n nodes and m edges. We consider subgraphs that have all nodes of the original graph and some of its edges. A subgraph is called Eulerian if each node has even degree. Your task is to count the number of Eulerian subgraphs modulo 10^9+7.

Input

The first input line has two integers n and m: the number of nodes and edges. The nodes are numbered 1,2,\dots,n. After this, there are m lines that describe the edges. Each line has two integers a and b: there is an edge between nodes a and b. There is at most one edge between two nodes, and each edge connects two distinct nodes.

Output

Print the number of Eulerian subgraphs modulo 10^9+7.

Constraints

$1 \le n \le 10^5$

$0 \le m \le 2$ \cdot 10^5$

$1 \le a,b \le n$

Example

Input

4 3
1 2
1 3
2 3

Output

2

Explanation: You can either keep or remove all edges, so there are two possible Eulerian subgraphs.