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 ca.

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 ≤ xN), 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




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