G. The Treetime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAbendsen 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:  If vertex v is white, mark it as black; otherwise, perform this operation on all direct sons of v instead.  Mark all vertices in the subtree of v (including v) as white.  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?InputThe 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.OutputFor each query of type 3, print "black" if the vertex is black; otherwise, print "white".ExamplesInput8 101 2 1 2 5 4 51 23 23 11 11 13 53 73 42 23 5OutputblackwhiteblackwhiteblackwhiteInput8 111 1 2 3 3 6 61 11 11 33 23 43 63 72 31 63 73 6OutputblackwhiteblackwhitewhiteblackNoteThe first example is shown on the picture below.  The second example is shown on the picture below.  
Input8 101 2 1 2 5 4 51 23 23 11 11 13 53 73 42 23 5
Outputblackwhiteblackwhiteblackwhite
['data structures', '*3200']