Solve the programming task below in a Python markdown code block.
A permutation of length N is an array of N integers A = [A_{1}, A_{2}, \dots, A_{N}] such that every integer from 1 to N appears in it exactly once.

We define a function over a permutation as follows:
F(A) = (A_{1} * A_{2}) + (A_{2} * A_{3}) + \cdots + (A_{N-2} * A_{N-1}) + (A_{N-1}*A_{N})

You are given an integer N. What is the expected value of the function F over all possible permutations of length N?

The expected value of the function can be represented as a fraction of the form \frac{P}{Q}. You are required to print P \cdot Q^{-1} \pmod{1 \, 000 \, 000 \, 007}. 

------ Input Format ------ 

- The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
- The first and only line of each test case contains a single integer N.

------ Output Format ------ 

For each test case, output on a single line the expected value of the function modulo 1 \, 000 \, 000 \, 007.

------ Constraints ------ 

$1 ≤ T ≤ 10^{5}$
$2 ≤ N ≤ 10^{9}$

----- Sample Input 1 ------ 
2
2
3
----- Sample Output 1 ------ 
2
333333343

----- explanation 1 ------ 
- Test Case $1$: There are $2$ possible permutations: $A = \{1, 2\}$ with $F(A) = 2$ and $A = \{2, 1\}$ with $F(A) = 2$. Hence the expected value of the function is $F(A) = \frac{1}{2} * 2 + \frac{1}{2} * 2 = 2$.

- Test Case $2$: There are $6$ possible permutations, with the value of function as $\{5, 5, 8, 8, 9, 9 \}$. Hence the expected value of the function is $F(A) = \frac{5+5+8+8+9+9}{6} = \frac{22}{3}$. The required output will be $333333343$, since $333333343 \cdot 3 \equiv 22 \pmod {1 \, 000 \, 000 \, 007}$.