Expectations on a Permutation ~ Multiplex Coder

A permutation of length

$N$ is an array of $N$ integers $A_{1}, A_{2}, \dots, A_{N}$ such that every integer from $1$ to $N$ appears in it exactly once.

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

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 $P \cdot Q^{- 1} (\mod 1 000 000 007)$ .

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

$1 \leq T \leq 10^{5}$
$2 \leq N \leq 10^{9}$

Sample Input 1

2
2
3

Sample Output 1

2
333333343

Explanation

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 $F (A) = \frac{5 + 5 + 8 + 8 + 9 + 9}{6} = \frac{22}{3}$ .