#undef _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#define fast ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define int long long
#define pb push_back
#define fi first
#define si second
#define ar array
typedef pair<int,int> pi;
typedef tuple<int,int,int> ti;
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {cerr << " " << to_string(H);debug_out(T...);}
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
int N, Q, root, post[100010], cnt = 1, par[100010][20], occ[100010], mn[100010];
vector<int> adj[100010];
priority_queue<pi, vector<pi>, greater<pi> > pq;
void dfs(int x, int p) {
par[x][0] = p;
for (int i = 1; i <= 17; ++i) {
if (par[x][i - 1] == -1) break;
par[x][i] = par[par[x][i - 1]][i - 1];
}
for (auto i: adj[x]) {
dfs(i, x);
}
post[x] = cnt++;
pq.push({post[x], x});
}
int kth_ancestor(int x, int k) {
for (int i = 0; i <= 17; ++i) {
if (x == -1) return -1;
if (k & (1 << i)) x = par[x][i];
}
return x;
}
void add(int x) {
int ret = 0;
for (int i = 0; i < x; ++i) {
ret = pq.top().si;
pq.pop();
occ[ret] = 1;
}
cout << ret << '\n';
}
void remove(int x) {
int lo = 0, hi = N + 1, up = x;
while (lo + 1 < hi) {
int mid = (lo + hi) / 2;
int node = kth_ancestor(x, mid);
if (node == -1 || occ[node] == 0) hi = mid;
else {
lo = mid;
up = node;
}
}
cout << lo << '\n';
occ[up] = 0;
pq.push({post[up], up});
}
void getmin(int x) {
mn[x] = x;
for (auto i: adj[x]) {
getmin(i);
mn[x] = min(mn[x], mn[i]);
}
}
signed main() {
fast;
cin >> N >> Q;
for (int i = 1; i <= N; ++i) {
int x; cin >> x;
if (x == 0) {
root = i;
continue;
}
adj[x].pb(i);
}
getmin(root);
for (int i = 1; i <= N; ++i) {
sort(adj[i].begin(), adj[i].end(), [](int x, int y) {
return mn[x] < mn[y];
});
}
memset(par, -1, sizeof par);
dfs(root, -1);
while (Q--) {
int op, x; cin >> op >> x;
if (op == 1) add(x);
else if (op == 2) remove(x);
}
return 0;
}
