**Time limit:**1.00 s**Memory limit:**512 MB

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.