4-cycle (Hard)

$N$ vertices and $M$ undirected edges form a simple graph $G$. In a simple graph, any two vertices are joined by at most one edge, and every edge connects two different vertices. The vertices of $G$ are numbered with positive integers from $1$ to $N$.

A simple cycle of length $L$ in $G$ is a sequence of vertices $\left( v_0,v_1,\cdots ,v_L \right)$ that satisfies the following conditions.

• For every $0 \leq i < L$, an edge connects $v_i$ and $v_{i+1}$ in $G$.
• For every $0 \leq i < j < L$, $v_i \neq v_j$, and $v_L = v_0$.

Two simple cycles are treated as the same cycle if one can be turned into the other with these operations.

• Reverse the sequence. That is, change $\left( v_0,v_1,\cdots ,v_L \right)$ to $\left( v_L,\cdots ,v_1,v_0 \right)$.
• Append the second element to the end and delete the first element. That is, change $\left( v_0,v_1,\cdots ,v_L \right)$ to $\left( v_1,\cdots ,v_L,v_1 \right)$.

For example, the simple cycles $\left( 1,2,3,4,1 \right)$ and $\left( 2,1,4,3,2 \right)$ are the same simple cycle. Count the distinct simple cycles of length $4$ in the graph $G$.

The first line contains two integers $N$ ($2 \leq N \leq 10^5$) and $M$ ($1 \leq M \leq 10^5$), separated by a space.

Each of the next $M$ lines contains two distinct vertices $u$ and $v$ ($1 \leq u,v \leq N$), separated by a space, which form an edge of $G$.

No edge is given more than once.

Print the number of distinct simple cycles of length $4$ in $G$, modulo $10^9+7$.

Note that $10^9+7$ is a prime number.