__ Problem:-__

You have become good friends with Chef. Right now, Chef is busy in the kitchen, so he asked you to solve a problem for him.

Consider a list of integers $\ufffd$. Initially, $\ufffd$ contains the integers $1$ through $\ufffd$, each of them exactly once (but it may contain multiple copies of some integers later). The order of elements in $\ufffd$ is not important. You should perform the following operation $\ufffd-1$ times:

- Choose two elements of the list, let's denote them by $\ufffd$ and $\ufffd$. These two elements may be equal.
- Erase the chosen elements from $\ufffd$.
- Append the number $\ufffd+\ufffd+\ufffd\cdot \ufffd$ to $\ufffd$.

At the end, $\ufffd$ contains exactly one integer. Find the maximum possible value of this integer. Since the answer may be large, compute it modulo $1,000,000,007$ ($1{0}^{9}+7$).

### Input

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

### Output

For each test case, print a single line containing one integer ― the maximum possible value of the final number in the list modulo $1{0}^{9}+7$.

### Constraints

- $1\le \ufffd\le 100,000$
- $1\le \ufffd\le 1,000,000$

### Subtasks

Subtask #1 (20 points): $1\le \ufffd,\ufffd\le 25$

Subtask #2 (80 points): original constraints

### Sample 1:

3 1 2 4

1 5 119

### Explanation:

Example case 1: $\ufffd=[1]$

Example case 2: $\ufffd=[1,2]\to [1+2+1\cdot 2]$

Example case 3: $\ufffd=[\mathbf{\text{1}},2,3,\mathbf{\text{4}}]\to [\mathbf{\text{2}},3,\mathbf{\text{9}}]\to [3,29]\to [119]$. The chosen elements in each step are in bold.

__Code(C++):-__

__Code(JAVA):-__

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