Problem: 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. 

<image> 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.

<image>

The second example is shown on the picture below.

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn = 100010;
int n, Q, head[maxn], to[maxn], nextt[maxn],
    tot = 1, block, pre[maxn], now[maxn], vis[maxn], tag[maxn], tag2[maxn];
struct node {
  int opt, x;
} e[maxn];
struct node2 {
  int v, white, dist;
};
vector<node2> V[maxn];
void add(int x, int y) {
  to[tot] = y;
  nextt[tot] = head[x];
  head[x] = tot++;
}
void dfs1(int u, int shang, int num, int d) {
  if (vis[u]) {
    if (shang) {
      node2 temp;
      temp.v = u;
      temp.white = num;
      temp.dist = d;
      V[shang].push_back(temp);
    }
    for (int i = head[u]; i; i = nextt[i]) {
      int v = to[i];
      dfs1(v, u, 0, 0);
    }
  } else {
    if (pre[u] == 0) num++;
    for (int i = head[u]; i; i = nextt[i]) {
      int v = to[i];
      dfs1(v, shang, num, d + 1);
    }
  }
}
void update1(int u) {
  if (!now[u]) {
    now[u] = 1;
    return;
  }
  tag[u]++;
  for (int i = 0; i < V[u].size(); i++) {
    node2 temp = V[u][i];
    if (temp.white + 1 <= tag[u]) update1(temp.v);
  }
}
void update2(int u) {
  now[u] = 0;
  tag[u] = 0;
  tag2[u] = 1;
  for (int i = 0; i < V[u].size(); i++) {
    node2 temp = V[u][i];
    V[u][i].white = temp.dist;
    update2(temp.v);
  }
}
void rebuild(int u, int num, int cover) {
  if (vis[u]) {
    num = tag[u];
    cover |= tag2[u];
  } else {
    now[u] = pre[u];
    if (cover) now[u] = 0;
    if (!now[u] && num) {
      now[u] = 1;
      num--;
    }
  }
  for (int i = head[u]; i; i = nextt[i]) {
    int v = to[i];
    rebuild(v, num, cover);
  }
}
int main() {
  scanf("%d%d", &n, &Q);
  for (int i = 2; i <= n; i++) {
    int x;
    scanf("%d", &x);
    add(x, i);
  }
  for (int i = 1; i <= Q; i++) scanf("%d%d", &e[i].opt, &e[i].x);
  block = sqrt(Q);
  for (int i = 1; i <= Q; i += block) {
    for (int j = 1; j <= n; j++) {
      vis[j] = tag[j] = tag2[j] = 0;
      pre[j] = now[j];
      V[j].clear();
    }
    for (int j = i; j <= min(Q, i + block - 1); j++) vis[e[j].x] = 1;
    dfs1(1, 0, 0, 0);
    for (int j = i; j <= min(Q, i + block - 1); j++) {
      int opt = e[j].opt, x = e[j].x;
      if (opt == 1) update1(x);
      if (opt == 2) update2(x);
      if (opt == 3) {
        if (now[x] == 1)
          puts("black");
        else
          puts("white");
      }
    }
    rebuild(1, 0, 0);
  }
  return 0;
}