An Olympian Math Problem(c++)

Question

Alice, a student of grade 66, is thinking about an Olympian Math problem, but she feels so despair that she cries. And her classmate, Bob, has no idea about the problem. Thus he wants you to help him. The problem is:

We denote k!k!:

k! = 1 \times 2 \times \cdots \times (k - 1) \times kk!=1×2×⋯×(k−1)×k

We denote SS:

S = 1 \times 1! + 2 \times 2! + \cdots +S=1×1!+2×2!+⋯+
(n - 1) \times (n-1)!(n−1)×(n−1)!

Then SS module nn is _
You are given an integer nn.

You have to calculate SS modulo nn.

Input
The first line contains an integer T(T \le 1000)T(T≤1000), denoting the number of test cases.

For each test case, there is a line which has an integer nn.

It is guaranteed that 2 \le n\le 10^{18}2≤n≤10 
18
 .

Output
For each test case, print an integer SS modulo nn.

Hint
The first test is: S = 1\times 1!= 1S=1×1!=1, and 11 modulo 22 is 11.

The second test is: S = 1\times 1!+2 \times 2!= 5S=1×1!+2×2!=5 , and 55 modulo 33 is 22.

Answer 1

2-->1
3-->2
4-->3
5-->4
试着找一下规律？