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 $10^9+7$ .

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.

• $1 \le n \le 10^5$
• $0 \le m \le 2 \cdot 10^5$
• $1 \le a,b \le n$

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