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G. The Tree
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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?

Input

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.

Output

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

Examples
Input
8 10
1 2 1 2 5 4 5
1 2
3 2
3 1
1 1
1 1
3 5
3 7
3 4
2 2
3 5
Output
black
white
black
white
black
white
Input
8 11
1 1 2 3 3 6 6
1 1
1 1
1 3
3 2
3 4
3 6
3 7
2 3
1 6
3 7
3 6
Output
black
white
black
white
white
black
Note

The first example is shown on the picture below.

The second example is shown on the picture below.