Äventyr 2

"Äventyr bortom tidpunkten, Sista Fiolen."

You travel between timelines to find the legendary violin of a forgotten country. Each timeline is a vertex of a tree, and an edge of the tree means you can move between the two timelines it joins. The timelines are numbered from $1$ to $N$. Some timelines hold the legendary violin and the rest do not. At the start, no timeline holds the violin. After the tree is given, process $Q$ queries of the following two kinds.

• 1 u: timeline $u$ becomes a timeline that holds the violin.
• 2 u: print the minimum number of edges a journey starting at timeline $u$ must cross to reach a timeline that holds the violin. If no timeline holds the violin, print $-1$.

The first line contains $N$ and $Q$. ($1 \le N, Q \le 10^5$)

The second line contains $N-1$ integers $A_2, A_3, \ldots, A_N$. $A_i$ means that the parent of timeline $i$ in the tree is timeline $A_i$. ($1 \le A_i \le N$, $A_i \ne i$) The given edges always form a single tree. When $N = 1$, the second line is empty.

Each of the next $Q$ lines contains one query in the form c v. If $c = 1$ it is a query of type 1, and if $c = 2$ it is a query of type 2. ($1 \le v \le N$) A query of type 1 is never given twice for the same timeline.

For every query of type 2, print its result on its own line, in order.