UVALive 5971

Problem J Permutation Counting

Dexter considers a permutation of first N natural numbers good if it doesn't have x and x+1 appearing consecutively, where (1 ≤ x < N)  For example, for N=3 , all goodpermutations are:

1. {1, 3, 2}

2.{2, 1, 3}

3.{3, 2, 1}

Input

Input starts with an integer T (≤ 10000 , denoting the number of test cases.Each

case starts with a line containing an integer N (1 ≤ N ≤ 106)

.

Output

For each case, print the case number and the number ofgoodpermutations

modulo1000 000 007

.

Sample Input

Output for Sample Input

3

2

3

5

Case 1: 1

Case 2: 3

Case 3: 53

 1 #include <map>

 2 #include <set>

 3 #include <list>

 4 #include <cmath>

 5 #include<cctype>

 6 #include <ctime>

 7 #include <deque>

 8 #include <stack>

 9 #include <queue>

10 #include <cstdio>

11 #include <string>

12 #include <vector>

13 #include<climits>

14 #include <cstdlib>

15 #include <cstring>

16 #include <iostream>

17 #include <algorithm>

18 #define LL long long

19 #define PI 3.1415926535897932626

20 using namespace std;

21 int gcd(int a, int b) {return a % b == 0 ? b : gcd(b, a % b);}

22 #define MAXN 1000005

23 #define MOD 1000000007

24 LL ans[MAXN],tmp[MAXN];

25 void init()

26 {

27     ans[1]=1;ans[2]=1;

28     for (int i=3;i<MAXN;i++)

29        {

30            ans[i]=((i-1)*ans[i-1])+(i-2)*ans[i-2];

31            ans[i]%=MOD;

32        }

33 }

34 int main()

35 {

36     init();

37     int T;int kase=1;

38     scanf("%d",&T);

39     while (T--)

40     {

41         int N;

42         scanf("%d",&N);

43         printf("Case %d: %lld\n",kase++,ans[N]);

44     }

45     return 0;

46 }

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