Game

Accepts: 138

Submissions: 358

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 131072/131072 K (Java/Others)

Problem Description

BrotherK is very rich. He has a big company.

One day, BrotherK wants to give an award to one of the employees in the company. It‘s so hard to make a choise that BrotherK decides to play a game to determine the lucky dog.

At the beginning of the game, all NN employees form a circle. Then, they receive t-shirts with numbers 1 through NN in clockwise order along the circle.

The game consists of many turns. In the ith turn, BrotherK starts by standing in front of a employee and announces a number X_iX?i??. He will move to the (X_i+1X?i??+1)th-next-employee in clockwise order, and the X_iX?i??th-next-employees will be removed from the circle, then the (i+1)th turn starts.

Attention that the 1th-next-employee of a employee is itself, and BrotherK stands in front of the employee with number 1 at first. In the ith turn, The value of X_iX?i?? is chosen randomly from a given integer set SS. When there is only one employee left in the game, the game ends and the employee wins the award.

You are given the int NN and the set of integers, BrotherK wants to know which employees are possible to win.

Input

The first line contains a single integer TT, indicating the number of test cases.

Each test case begins with two integer N, MN,M, indicating the number of employees in BrotherK‘s company, and the size of BrotherK‘s integer set SS. Next line contains MM numbers, from a_1a?1?? to a_Ma?M??, indicating the integer in SS.

TT is about 50

1~\le~N, M~\le~2001 ≤ N,M ≤ 200

1~\le~a_i~\le~10^91 ≤ a?i?? ≤ 10?9??

Output

For each test, print two lines.

The first line contains a integer KK, indicating how many people are possible to win.

The second line contains KK number, indicating the number in T-shirt who can win, in ascending order.

Sample Input

2
3 1
1
3 2
1 2

Sample Output

1
3
3
1 2 3思路：dp+约瑟夫环；约瑟夫环的问题可以用递推来解决，ans[n] = (ans[n-1]+m)%n;那么这次每次可以有多个间隔，那么dp[i][j]表示当执行第n-i+1次时下标为j是否存在；具体过程看代码

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<string>
 5 #include<cmath>
 6 #include<cstdlib>
 7 #include<queue>
 8 #include<stack>
 9 #include<map>
10 #include<vector>
11 #include<algorithm>
12 using namespace std;
13 typedef long long LL;
14 bool flag[10000];
15 int dp[205][205];
16 int ask[1000];
17 int main(void)
18 {
19     int T;
20     scanf("%d",&T);
21     while(T--)
22     {
23         int n,m;
24         memset(flag,0,sizeof(flag));
25         scanf("%d %d",&n,&m);
26         int i,j;
27         memset(dp,-1,sizeof(dp));
28         for(i = 2; i < 205; i++)
29         {
30             for(j = 0; j < 205; j++)
31             {
32                 dp[i][j] = -1;
33             }
34         }
35         for(i = 0; i < m; i++)
36         {
37             scanf("%d",&ask[i]);
38         }
39         dp[1][0] = 1;
40         for(i = 2; i <= n; i++)
41             for(j = 0; j <= i; j++)
42                 if(dp[i-1][j]!=-1)
43                     for(int s = 0; s < m; s++)
44                         dp[i][(j+ask[s])%i] = 1;
45         int sum = 0;
46         int ac[1000];
47         for(i = 0; i < n; i++)
48         {
49             if(dp[n][i]==1)
50             {
51                 ac[sum++] = i+1;
52             }
53         }
54         printf("%d\n",sum);
55         printf("%d",ac[0]);
56         for(i = 1; i < sum; i++)
57             printf(" %d",ac[i]);
58         printf("\n");
59     }
60     return 0;
61 }