Finding Your Roots

P-22's father was P-1, the first mountain lion tagged in the Santa Monica Mountains. P-22's mother is unknown. Unfortunately, we do not know anything about P-1's parents, so we can only trace back P-22's ancestry two generations (himself and his father). In some other cases, one can trace back ancestry quite a bit further, and you are supposed to find out just how far.

To keep things simple (and avoid exponential growth), each mountain lion is given only one parent, or none when no information is available. Return the total number of generations in the ancestry of a specific mountain lion that can be traced back.

The first line contains the number of data sets $1 \le K \le 100$. This is followed by $K$ data sets.

The first line of a data set contains two integers $1 \le L \le n \le 10000$. $n$ is the total number of mountain lions in the database, and $L$ is the mountain lion whose ancestry you are interested in.

The next line contains $n$ integers $p_i$, where $0 \le p_i \le n$ is the parent of mountain lion $i$. A $0$ means the parent of lion $i$ is unknown. Because these are parent relationships, the input never contains cycles.

For each data set, print Data Set x: on its own line, where $x$ is the data set number. Then print the number of generations of the ancestry of $L$ that are in the database, including $L$ himself or herself.

Print a blank line after each data set.