B. Emordnilaptime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array), and [1,3,4] is also not a permutation (n=3 but there is 4 in the array). There are n! = n \cdot (n-1) \cdot (n - 2) \cdot \ldots \cdot 1 different permutations of length n.Given a permutation p of n numbers, we create an array a consisting of 2n numbers, which is equal to p concatenated with its reverse. We then define the beauty of p as the number of inversions in a.The number of inversions in the array a is the number of pairs of indices i, j such that i < j and a_i > a_j.For example, for permutation p = [1, 2], a would be [1, 2, 2, 1]. The inversions in a are (2, 4) and (3, 4) (assuming 1-based indexing). Hence, the beauty of p is 2.Your task is to find the sum of beauties of all n! permutations of size n. Print the remainder we get when dividing this value by 1\,000\,000\,007 (10^9 + 7).InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 10^5). The description of the test cases follows.Each test case has only one line — the integer n (1 \leq n \leq 10^5).It is guaranteed that the sum of n over all test cases does not exceed 10^5.OutputFor each test case, print one integer — the sum of beauties of all permutations of size n modulo 1\,000\,000\,007 (10^9 + 7).ExampleInput
312100Output
0
4
389456655
NoteFor the first test case of the example, p = [1] is the only permutation. a = [1, 1] has 0 inversions.For the second test case of the example, the permutations are [1, 2] and [2, 1]. Their respective a arrays are [1, 2, 2, 1] and [2, 1, 1, 2], both of which have 2 inversions.
312100
0 4 389456655 
['combinatorics', 'greedy', 'math', '*900']