"Bless of Stiff Waist Beast" is a computer virus that will cause the infected computer unable to operate properly. Please help us to calculate the number of infected computers.
The virus is spreading in a network of computers. The network is a tree with $N$ nodes, each node represents a computer. The nodes are numbered from $1$ to $N$ and node $1$ is the root of the tree. Each second, the virus will spread from each infected node to all its children. Initially, only node $1$ is infected. Please calculate the number of infected nodes after $K$ seconds.
The first line contains two integers \(N\) and \(K\), indicating the number of nodes and the number of seconds passed. For the following \(N\) lines:
The \(i\)-th line starts with an integer \(M_i\), indicating the number of children of node \(i\). The following \(M_i\) integers \(c_{i,1}, c_{i,2}, \ldots, c_{i,M_i}\) indicate the children of node \(i\).
\(N \quad K\)
\(M_1 \quad c_{1,1} \quad c_{1,2} \quad \ldots \quad c_{1,M_1}\)
\(M_2 \quad c_{2,1} \quad c_{2,2} \quad \ldots \quad c_{2,M_2}\)
\(\enspace \vdots\)
\(M_N \quad c_{N,1} \quad c_{N,2} \quad \ldots \quad c_{N,M_N}\)
\(1 \le N \le 5 \times 10^5\)
\(1 \le K \le 5 \times 10^5\)
\(1 \le M_i \le N-1\)
\(\sum_{i=1}^{N}{M_i} = N-1\)
\(1 \le c_{i,j} \le N\)
Output one integer indicating the number of infected nodes after $K$ seconds.
You should print a newline('\n') character at the end of output.