#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif
// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif
//#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define endl '\n'
#define FF first
#define SS second
#define all(a) a.begin(), a.end()
#define mod (ll)(1000000007)
const int lg=20;
int n, q, cur;
vector<int>P, Has_ball, Mn;
vector<vector<int> >A, Up;
priority_queue<array<int, 2> >pq;
map<int, int>mp;
void pre(){
P.clear(), Has_ball.clear(), Mn.clear(), A.clear(), Up.clear(), mp.clear();
P.resize(n+1), Has_ball.resize(n+1), Mn.resize(n+1), A.resize(n+1), Up.resize(n+1, vector<int>(lg+1));
}
bool cmp(int a, int b){
return Mn[a]<Mn[b];
}
void dfs(int u){
Mn[u]=u;
Up[u][0]=P[u];
for(int j=1;j<=lg;j++){
Up[u][j]=Up[Up[u][j-1]][j-1];
}
for(auto v:A[u]){
dfs(v);
Mn[u]=min(Mn[u], Mn[v]);
}
sort(all(A[u]), cmp);
}
void ord(int u){
for(auto v:A[u]){
ord(v);
}
mp[u]=cur;
array<int, 2>a={-cur, u};
pq.push(a);
cur++;
}
int main(){
ios_base::sync_with_stdio(0);cin.tie(0);
cin>>n>>q;
pre();
int root;
for(int i=1;i<=n;i++){
int p, u=i;
cin>>p;
if(!p)
root=u;
else{
A[p].push_back(u);
P[u]=p;
}
}
dfs(root), ord(root);
while(q--){
int type, k;
cin>>type>>k;
int ans=0;
if(type==1){
// add k balls and print the last postion
while(k--){
int u=pq.top()[1];
pq.pop();
Has_ball[u]=1;
ans=u;
}
}
else if(type==2){
// remove ball in node k and print the number of balls in nodes above node k
for(int j=lg;j>=0;j--){
int v=Up[k][j];
if(Has_ball[v])
ans+=(1<<j), k=v;
}
Has_ball[k]=0;
array<int, 2>a={-mp[k], k};
pq.push(a);
}
cout<<ans<<endl;
}
}
