F - A Very Easy Graph Problem HDU - 6832 未解决

An undirected connected graph has $n$ nodes and $m$ edges, The $i$-th edge’s length is $2^i$. Each node $i$ has a value $a_i$, which is either $0$ or $1$. You need to calculate:

$$
\sum_{i=1}^{n}\sum_{j=1}^{n}d(i,j)\times [a_i=1\wedge a_j=0]
$$

$d(i,j)$ indicates the shortest distance between $i$ and $j$. $[\ ]$ is the Iverson bracket. $\wedge$ indicates $\texttt{AND}$.

Because the answer may be too large, please output the answer modulo $10^9 + 7$.

InputThe first line contains one integer $T$($1\le T \le 8$)，indicating the number of test cases.

The second line contains two ingeters $n,m$($1\le n\le 10^5,1\le m\le 2\times 10^5$).

The third line contains $n$ positive integers $a_1,a_2,...,a_n(a_i = 0$ or $1$) —— the value of the nodes.

The following $m$ lines contain two ingeters $u,v(1
\le u,v \le n)$, and the $i$-th line represents the i-th undirected edge’s length is $2^i$, between node $u$ and $v$.

The sum of $n,m$ is no more than $2\times 10^5$.OutputPrint a single integer—— the value of the answer modulo $10^9+7$.Sample Input

1
3 2
0 1 0
3 1
3 2

Sample Output

10

Sponsor

题意：

给出一个无向连通图，里面的点分为0号点和1号点，第i条边的边权是2的i次。

询问所有1号点到0号点的最短路径之和。

题解：

　　建树，最短路径都在图的最小生成树上

　　统计单边的贡献：

　　　　一边跑一边计数 乘上边权值

附代码（未通过，待解决）