A11880. The Tree

Abendsen assigned a mission to Juliana. In this mission, Juliana has a rooted tree with $n$ vertices. Vertex number $1$ is the root of this tree. Each vertex can be either black or white. At first, all vertices are white. Juliana is asked to process $q$ queries. Each query is one of three types:

1. If vertex $v$ is white, mark it as black; otherwise, perform this operation on all direct sons of $v$ instead.
2. Mark all vertices in the subtree of $v$ (including $v$ ) as white.
3. Find the color of the $i$ -th vertex.

An example of operation "1 1" (corresponds to the first example test). The vertices $1$ and $2$ are already black, so the operation goes to their sons instead.Can you help Juliana to process all these queries?

The first line contains two integers $n$ and $q$ ( $2\leq n\leq 10^5$ , $1\leq q\leq 10^5$ ) — the number of vertices and the number of queries.

The second line contains $n-1$ integers $p_2, p_3, \ldots, p_n$ ( $1\leq p_i<i$ ), where $p_i$ means that there is an edge between vertices $i$ and $p_i$ .

Each of the next $q$ lines contains two integers $t_i$ and $v_i$ ( $1\leq t_i\leq 3$ , $1\leq v_i\leq n$ ) — the type of the $i$ -th query and the vertex of the $i$ -th query.

It is guaranteed that the given graph is a tree.

For each query of type $3$ , print "black" if the vertex is black; otherwise, print "white".

The first example is shown on the picture below.

The second example is shown on the picture below.