#include <bits/stdc++.h>
using namespace std;
#define SZ(s) (int)s.size()
#define ff first
#define ss second
int n, q;
vector <vector <int>> v, sp;
vector <int> m, v1, b, vis;
void dfs(int x, int y){
m[x] = x;
for(auto i : v[x]){
if(i == y) continue;
dfs(i, x);
m[x] = min(m[x], m[i]);
}
return;
}
void df(int x, int y){
vector <pair<int,int>> v2;
for(auto i : v[x]){
if(i == y) continue;
v2.push_back({m[i], i});
}
sort(v2.begin(), v2.end());
for(int i = 0; i < SZ(v2); i++){
df(v2[i].ss, x);
}
v1.push_back(x);
}
int d(int x){
int cnt = 0;
for(int i = 20; i >= 0; i--){
int k = sp[x][i];
if(vis[k] == 1) x = k, cnt += (1<<i);
}
cout << cnt << "\n";
return x;
}
int main(){
ios::sync_with_stdio(false); cin.tie(nullptr);
cin >> n >> q;
int root = 1;
v.resize(n+1), m.resize(n+1);
sp.resize(n+1, vector <int> (25));
vector <int> a(n+1);
for(int i = 1; i <= n; i++){
cin >> a[i];
sp[i][0] = a[i];
if(a[i] == 0) root = i;
else {
v[a[i]].push_back(i);
v[i].push_back(a[i]);
}
}
dfs(root, 0);
df(root, 0);
set <pair<int,int>> s;
b.resize(n+1), vis.resize(n+1,0);
for(int i = 0; i < SZ(v1); i++){
s.insert({i, v1[i]});
b[v1[i]] = i;
}
for(int j = 1; j <= 20; j++){
for(int i = 1; i <= n; i++){
sp[i][j] = sp[sp[i][j-1]][j-1];
}
}
while(q--){
int t, x;
cin >> t >> x;
if(t == 1){
int k;
while(x--){
k = (*s.begin()).ss;
vis[k] = 1;
s.erase(s.begin());
}
cout << k << '\n';
}
else {
int k = d(x);
vis[k] = 0;
s.insert({b[k], k});
}
}
}
