KOSARE - KOSARE


 

Mirko found N boxes with various forgotten toys at his attic. There are M different toys, numbered 1 
through M, but each of those can appear multiple times across various boxes.
Mirko decided that he will choose some boxes in a way that there is at least one toy of each kind
present, and throw the rest of the boxes away.
Determine the number of ways in which Mirko can do this.

 

Mirko found N boxes with various forgotten toys at his attic. There are M different toys, numbered 1 

through M, but each of those can appear multiple times across various boxes.

Mirko decided that he will choose some boxes in a way that there is at least one toy of each kind

present, and throw the rest of the boxes away.

Determine the number of ways in which Mirko can do this.

 

 

Input

 

The first line of input contains two integers N and M (1 ≤ N ≤ 1 000 000, 1 ≤ M ≤ 20).

Each of the following N lines contains an integer Ki (0 ≤ Ki ≤ M) followed by Ki distinct integers from 

interval [1, M], representing the toys in that box.

 

Output

The first and only line of output should contain the requested number of ways modulo 1 000 000 007.

Example

Input 1:
3 3
3 1 2 3
3 1 2 3
3 1 2 3

Output 1:
7
Input 2:
3 3
1 1
1 2
1 3

Output 2:
1
Input 3:
4 5
2 2 3
2 1 2
4 1 2 3 5
4 1 2 4 5

Output 3:
6

hide comments
TINYJR: 2013-01-02 05:45:51

Fread is expected in this problem.

Edit: You can get AC using scanf

Last edit: 2013-01-02 06:47:34
(Tjandra Satria Gunawan)(曾毅昆): 2012-12-31 19:20:08

TLE!


Added by:UNI Training
Date:2012-12-31
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:COCI 2011-2012 Contest #6