\problemname{Bye Bye Bilbo}

\newcommand{\maxn}{10^5}

Bilbo Baggins is finally leaving the Shire! To celebrate his departure, Gandalf 
plans to set up a spectacular display of fireworks across the land.

The Shire has $n$ hobbit holes numbered $1$ to $n$, each of which is occupied
by exactly one hobbit. Every hole $i > 1$ is connected by a lane directly to a
unique hole $p_i$, with $p_i < i$, so that following the lanes always leads
towards hole $1$, the town.

\begin{figure}[!h]
    \centering
    \includegraphics{figure.pdf}
    \caption{Illustration of the first sample.}
    \label{fig:sample}
\end{figure}

Gandalf must place fireworks at a minimum number of hobbit holes so that every 
hobbit can see at least one firework. The fireworks have a visibility range $k$.
A hobbit at hole $i$ can see a firework placed at hole $j$ if it is placed at 
their own hole, or if $j$ lies on the path from hole $i$ to the town and the
number of lanes between $i$ and $j$ is strictly less than $k$.

\begin{Input}
    The input consists of:
    \begin{itemize}
        \item One line with two integers $n$ and $k$ ($2 \leq n \leq \maxn$, $1 \le k \le n$), the number of hobbit holes and the firework range.
        \item One line with $n-1$ integers $p_2, p_3, \ldots, p_n$ ($1 \le p_i \leq i-1$), where $p_i$ is the next hole reached when going from hole $i$ toward the town.
    \end{itemize}
\end{Input}

\begin{Output}
    Output one integer $m$, the minimum number of hobbit holes
    where a firework must be placed, followed by $m$ distinct
    integers, the indices of those holes.

    If there are multiple ways to place the fireworks using the minimum number of 
    holes, you may output any one of them.
\end{Output}

\remainingsamples

In the first sample, a firework at hole $1$, i.e. the town, can only be seen by
the hobbits at holes $1$, $2$, $3$, and $4$. A second firework at hole $5$ can
only be seen by the hobbit at hole $5$.

In the second sample, a firework at hole $1$ can only be seen by the hobbits at
holes $1$, $2$, and $3$. A second firework at hole $3$ can only be seen by the
hobbits at holes $3$, $4$, $5$, and $6$. So every hobbit can see at least one
firework.
