Road To The 3rd Building 未解决
https://vjudge.net/contest/387998#problem/A
Kanade takes responsibility to improve this status. She thinks it a good idea to decorate the ginkgo trees along the road to the 3rd Building, making them cute. There are $n$ ginkgo trees that are planted along the road, numbered with $1\ldots n$. Each tree has a cute value. The cute value of tree $i$ is $s_i$.
Kanade defines a plan as an ordered pair $(i,j)$, here $1\le i\le j\le n$. It means a student will appear at the position of the tree $i$ magically, walk along the road, and finally stop walking at the position of the tree $j$. The cute level of a plan is the average of the cute value of the trees visited. Formally, the cute level of plan $(i,j)$ is $\frac{1}{j-i+1}\sum_{k=i}^j s_k$.
Kanade wants to know the mathematical expectation of the cute level if a student will take a plan among all these plans in a uniformly random way. But she is busy with learning Computer Networking, would you help her?
InputThe first line of the input contains an integer $T$ — the number of testcases. You should process these testcases independently.
The first line of each testcase contains an integer $n$ — the number of ginkgo trees.
The second line of each testcase contains $n$ integers $s_i$ — the cute value of each ginkgo tree, space-separated.
$1\le T\le 20,1\le n\le 2\times 10^5,1\le s_i\le 10^9$
It is guaranteed that $\sum n\le 10^6$.OutputFor each testcase, output the answer in the fraction form modulo $10^9+7$ in one line. That is, if the answer is $\frac{P}{Q}$, you should output $P\cdot Q^{-1}\bmod (10^9+7)$, where $Q^{-1}$ denotes the multiplicative inverse of $Q$ modulo $10^9+7$.Sample Input
3 3 1 3 2 6 1 1 4 5 1 4 9 7325 516 56940 120670 16272 15007 337527 333184 742294
Sample Output
83333336 188888893 303405448
题意：
给n个数的序列，现在任意选择一个区间定义一个平均值
求出这个平均值的期望
思路：
参考：https://blog.csdn.net/fztsilly/article/details/107847396
找规律
k = 1项和k = n项分子相同
s[n−1] ，
（s[n−1]+s[n]）/ 2 ，
...，
（s[1] + s[2]+...+s[n]）/n
每次对分母取逆元
（有奇数项，另外加上最中间的数？
未通过
