Kill Demodogs
Description
Demodogs from the Upside-down have attacked Hawkins again. El wants to reach Mike and also kill as many Demodogs in the way as possible.
Hawkins can be represented as an $n \times n$ grid. The number of Demodogs in a cell at the $i$-th row and the $j$-th column is $i \cdot j$. El is at position $(1, 1)$ of the grid, and she has to reach $(n, n)$ where she can find Mike.
The only directions she can move are the right (from $(i, j)$ to $(i, j + 1)$) and the down (from $(i, j)$ to $(i + 1, j)$). She can't go out of the grid, as there are doors to the Upside-down at the boundaries.
Calculate the maximum possible number of Demodogs $\mathrm{ans}$ she can kill on the way, considering that she kills all Demodogs in cells she visits (including starting and finishing cells).
Print $2022 \cdot \mathrm{ans}$ modulo $10^9 + 7$. Modulo $10^9 + 7$ because the result can be too large and multiplied by $2022$ because we are never gonna see it again!
(Note, you firstly multiply by $2022$ and only after that take the remainder.)
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \leq t \leq 10^4$). Description of the test cases follows.
The first line of each test case contains one integer $n$ ($2 \leq n \leq 10^9$) — the size of the grid.
For each test case, print a single integer — the maximum number of Demodogs that can be killed multiplied by $2022$, modulo $10^9 + 7$.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \leq t \leq 10^4$). Description of the test cases follows.
The first line of each test case contains one integer $n$ ($2 \leq n \leq 10^9$) — the size of the grid.
Output
For each test case, print a single integer — the maximum number of Demodogs that can be killed multiplied by $2022$, modulo $10^9 + 7$.
4
2
3
50
1000000000
14154
44484
171010650
999589541
Note
In the first test case, for any path chosen by her the number of Demodogs to be killed would be $7$, so the answer would be $2022 \cdot 7 = 14154$.