398. Friends of Friends

Time limit per test: 0.25 second(s)
Memory limit: 65536 kilobytes
input: standard
output: standard



Social networks are very popular now. They use different types of relationships to organize individual users in a network. In this problem friendship is used as a method to connect users. For each user you are given the list of his friends. Consider friendship as a symmetric relation, so if user a is a friend of user b then b is a friend of a.

A friend of a friend for a is such a user c that c is not a friend of a, but there is such b that b is a friend of a and c is a friend of b. Obviously c ≠ a.

Your task is to find the list of friends of friends for the given user x.

Input
The first line of the input contains integer numbers N and x (1 ≤ N ≤ 50, 1 ≤ x ≤ N), where N is the total number of users and x is user to be processed. Users in the input are specified by their numbers, integers between 1 and N inclusive. The following N lines describe friends list of each user. The i-th line contains integer di (0 ≤ di ≤ 50) — number of friends of the i-th user. After it there are di distinct integers between 1 and N — friends of the i-th user. The list doesn't contain i. It is guaranteed that if user a is a friend of user b then b is a friend of a.

Output
You should output the number of friends of friends of x in the first line. Second line should contain friends of friends of x printed in the increasing order.

Example(s)
sample input
 
sample output
 
4 2
1 2
2 1 3
2 4 2
1 3

1
4


sample input
 
sample output
 
4 1
3 4 3 2
3 1 3 4
3 1 2 4
3 1 2 3

0