CF1017G 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

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.