7593: Resistance

You are given a cactus with n vertices and m edges. There is a 1 Ohm resistor on every edge.

Let f(s,t) be the equivalent resistance between the vertex s and the vertex t .

Print ∑1≤s<t≤nf(s,t) .

Note: a cactus (sometimes called a cactus tree) is a connected graph in which any two simple cycles have at most one vertex in common. Equivalently, it is a connected graph in which every edge belongs to at most one simple cycle.

For each test case, print the answer modulo 109+7 . That is,the answer can be represented as a fraction a/b where (a,b)=1 , output c(0≤c<109+7) such that bc≡a(mod109+7) .