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?

Input

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

The second line contains n-1 integers p_2, p_3, …, p_n (1≤ 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≤ t_i≤ 3, 1≤ v_i≤ 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.

inputFormat

Input

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

The second line contains n-1 integers p_2, p_3, …, p_n (1≤ 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≤ t_i≤ 3, 1≤ v_i≤ 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.

outputFormat

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.

样例

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

black
white
black
white
black
white

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