A. An Olympian Math Problem

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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≤1018.

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.

樣例輸入復制

2
2
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樣例輸出復制

1
2

題目來源

ACM-ICPC 2018 南京賽區網絡預賽

題意很好理解。

直接代碼

代碼:

 1 //A-數學公式
 2 #include<iostream>
 3 #include<cstdio>
 4 #include<cstring>
 5 #include<algorithm>
 6 #include<bitset>
 7 #include<cassert>
 8 #include<cctype>
 9 #include<cmath>
10 #include<cstdlib>
11 #include<ctime>
12 #include<deque>
13 #include<iomanip>
14 #include<list>
15 #include<map>
16 #include<queue>
17 #include<set>
18 #include<stack>
19 #include<vector>
20 using namespace std;
21 typedef long long ll;
22 
23 const double PI=acos(-1.0);
24 const double eps=1e-6;
25 const ll mod=1e9+7;
26 const int inf=0x3f3f3f3f;
27 const int maxn=1e5+10;
28 const int maxm=100+10;
29 #define ios ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
30 //公式為1*1！+2*2！+3*3!+...+n*n!=(n+1)!-1,本題為(n!-1)%n
31 //因為n!-1=(n-1)*n-1=(n-2)*n+n-1,所以[(n-2)*n+(n-1)]%n=n-1
32 //因n*n!=(n+1-1)n!=(n+1)n!-n!=（n+1)!-n!
33 //所以：1*1!=2!-1!
34 //2*2!=3!-2!
35 //3*3!=4!-3!
36 //.
37 //n*n!=(n+1)!-n!
38 //相加後有：1*1!+2*2!+3*3!+.+n*n!=（n+1)!-1
39 //1*1!+2*2!+3*3!+.+n*n!=（n+1)!-1
40 //把最後一項拆開來,變成(n+1-1)n!=(n+1)n!-n!
41 
42 int main()
43 {
44     int t;
45     cin>>t;
46     while(t--){
47         ll n;
48         cin>>n;
49         cout<<n-1<<endl;
50     }
51 }

溜了，一會貼一下線段樹的題目。

計蒜客 ACM-ICPC 2018 南京賽區網絡預賽 A. An Olympian Math Problem-數學公式題