Kill Demodogs (Codeforces 1731B)
Tags: Greedy, math

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.)

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 $$$10^9 + 7$$$.

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 $$$2022 \cdot 7 = 14154$$$.

Sample Inputs:
4
2
3
50
1000000000

Sample Outputs:
14154
44484
171010650
999589541

Solution (Python):
for i in [*open(0)][1:]:
    i = int(i)
    print((i + 1) * (4 * i * i - i) * 337 % (10 ** 9 + 7))

Solution (Python):
for i in [*open(0)][1:]:
    i = int(i)
    print((i + 1) * (4 * i * i - i) * 337 % (10 ** 9 + 7))

Solution (Python):
for i in [*open(0)][1:]:
    i = int(i)
    print((i + 1) * (4 * i * i - i) * 337 % (10 ** 9 + 7))