#include <bits/stdc++.h>
using namespace std;
const int nmax = 1e5 + 5;
set<int> s;
vector<int> in[nmax], adj[nmax];
bool f[nmax];
int mps[nmax], v[nmax], to[nmax], back[nmax];
int up[nmax][17], d[nmax];
void dfs1(int i, int tata = 0) {
mps[i] = i;
for(auto it : in[i]) {
if(it != tata) {
dfs1(it, i);
mps[i] = min(mps[i], mps[it]);
}
}
}
int timp = 1;
bool cmp(int a, int b) {
return mps[a] < mps[b];
}
void dfs2(int i, int tata = 0) {
sort(in[i].begin(), in[i].end(), cmp);
for(auto it : in[i]) {
if(it != tata) {
dfs2(it, i);
}
}
to[i] = timp;
back[timp] = i;
timp++;
}
void dfs(int i, int tata = 0) {
up[i][0] = tata;
for(int j = 1; (1 << j) <= d[i]; j++) {
up[i][j] = up[up[i][j - 1]][j - 1];
}
for(auto it : adj[i]) {
if(it != tata) {
d[it] = d[i] + 1;
dfs(it, i);
}
}
}
int qry(int a) {
int ans = 0;
for(int i = 16; i >= 0; i--) {
if((1 << i) <= d[a] && f[up[a][i]] == 0) {
a = up[a][i];
ans += (1 << i);
}
}
cout << ans << '\n';
return a;
}
int32_t main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int n, q, root = -1;
cin >> n >> q;
for(int i = 1; i <= n; i++) {
s.insert(i);
f[i] = 1;
int a;
cin >> a;
if(a == 0) {
root = i;
continue;
}
in[a].push_back(i);
in[i].push_back(a);
}
dfs1(root);
dfs2(root);
for(int i = 1; i <= n; i++) {
for(auto it : in[i]) {
adj[to[i]].push_back(to[it]);
adj[to[it]].push_back(to[i]);
}
}
dfs(n);
while(q--) {
int t, a;
cin >> t >> a;
if(t == 1) {
int ult = 0;
while(a--) {
ult = *s.begin();
f[ult] = 0;
s.erase(ult);
}
cout << back[ult] << '\n';
} else {
int x = qry(to[a]);
s.insert(x);
f[x] = 1;
}
}
return 0;
}
