CSES - Eulerian Subgraphs
  • Time limit: 1.00 s
  • Memory limit: 512 MB

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.


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



4 3
1 2
1 3
2 3



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