- 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 $10^9+7$.
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.
Print the number of Eulerian subgraphs modulo $10^9+7$.
- $1 \le n \le 10^5$
- $0 \le m \le 2 \cdot 10^5$
- $1 \le a,b \le n$
Explanation: You can either keep or remove all edges, so there are two possible Eulerian subgraphs.