#include <bits/stdc++.h>
using namespace std;
const int N = 100'000 + 7, L = 20 + 7;
vector<int> ord, adj[N];
int n, q, r, mn[N], idx[N], sp[L][N];
bool mark[N];
set<int> s;
void read_input() {
cin >> n >> q;
for (int i = 1; i <= n; i++) {
int p;
cin >> p;
if (p == 0) {
r = i;
} else {
adj[i].push_back(p);
adj[p].push_back(i);
}
}
}
void dfs1(int v, int p) {
mn[v] = v;
for (int u : adj[v])
if (u != p) {
dfs1(u, v);
mn[v] = min(mn[v], mn[u]);
}
}
void dfs2(int v, int p) {
sort(adj[v].begin(), adj[v].end(), [](int v1, int v2) -> bool { return mn[v1] < mn[v2]; });
for (int u : adj[v])
if (u != p)
dfs2(u, v);
ord.push_back(v);
}
void dfs3(int v, int p) {
sp[0][v] = p;
for (int i = 1; i < L; i++) {
if (sp[i - 1][sp[i - 1][v]] == 0)
break;
else
sp[i][v] = sp[i - 1][sp[i - 1][v]];
}
for (int u : adj[v])
if (u != p)
dfs3(u, v);
}
void pre_process() {
dfs1(r, 0);
ord.push_back(-1);
dfs2(r, 0);
dfs3(r, 0);
for (int i = 1; i <= n; i++)
idx[ord[i]] = i;
for (int i = 1; i <= n; i++)
s.insert(i);
}
void add(int x) {
for (int i = 1; i <= x; i++) {
int t = *s.begin();
s.erase(t);
mark[t] = true;
if (i == x)
cout << ord[t] << '\n';
}
}
void remove(int v) {
int res = 0, u = v;
for (int i = L - 1; i >= 0; i--)
if (mark[idx[sp[i][u]]]) {
u = sp[i][u];
res |= (1 << i);
}
mark[idx[u]] = false;
s.insert(idx[u]);
cout << res << '\n';
}
void solve() {
while (q--) {
int t, x;
cin >> t >> x;
if (t == 1)
add(x);
else
remove(x);
}
}
int main() {
ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
read_input();
pre_process();
solve();
}
