F

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:

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

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

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

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

The second line contains two ingeters $n,m$($1le nle 10^5,1le mle 2 imes 10^5$).

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 $2 imes 10^5$.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）