CF1731B Kill Demodogs

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 $ .

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 $ .