Problem Statement

$N$ integers $A_1,A_2, \cdots\ ,A_N$ are written on a blackboard.

You perform the following operation $N-1$ times, reducing the numbers written on the blackboard to $1$ number.
・Choose $2$ of the numbers written on the blackboard uniformly at random. These $2$ numbers must be written in different places. Then, newly write on the blackboard the number obtained by adding together the sum and the product of the chosen $2$ numbers, and erase the chosen $2$ numbers from the blackboard.

Find the expected value of the $1$ number remaining at the end, after the $N-1$ operations.

Here, it is guaranteed that the expected value is a rational number greater than or equal to $0$.
If the expected value is $0$, output $0$.
Otherwise, it can be proved under the constraints of this problem that the expected value can be represented as an irreducible fraction $\frac{P}{Q}$ using integers $P,Q$ greater than or equal to $1$, and that there uniquely exists an integer $X$ such that $X \times Q \equiv P(\rm{mod} 10^9+7)$ and $0 \leq X < 10^9+7$. Output such an $X$.

$T$ test cases are given. Answer all of the test cases.

Input

$T$

$N$
$A_1\ A_2\ \cdots\ A_N$

・$1 \leq T \leq 100$
・$2 \leq N \leq 100$
・$0 \leq A_i \leq 200 (1 \leq i \leq N)$
・All inputs are integers

Output

Output $T$ lines. On the $i$-th line, output the expected value for the $i$-th test case modulo $\rm{mod} 10^9+7$, followed by a newline.

Sample

2
3
1 1 0
2
1 1

3
3