#include<bits/stdc++.h>
using namespace std;
#define int long long
#define maxn 100050
vector<vector<int> > adj(maxn);
vector<int> mini(maxn,-1);
vector<int> fenwick(maxn,0);
vector<int> num(maxn,0);
vector<int> ipos(maxn,0);
#define f first
#define s second
int parents[18][maxn];
void add(int a){
int pos = a+1;
while(pos<fenwick.size()){
fenwick[pos] += 1;
pos += pos&(-pos);
}
return;
}
void add2(int a){
int pos = a+1;
while(pos<fenwick.size()){
fenwick[pos] -= 1;
pos += pos&(-pos);
}
return;
}
int query(int a,int b){
int sum = 0;
b++;
while(b>0){
sum += fenwick[b];
b -= b&(-b);
}
while(a>0){
sum -= fenwick[a];
a -= a&(-a);
}
return sum;
}
void dfs1(int node,int parent){
parents[0][node] = parent;
for(auto k:adj[node]){
if(k!=parent){
dfs1(k,node);
}
}
mini[node] = node;
vector<pair<int,int> > vect1;
for(auto k:adj[node]){
if(k!=parent){
vect1.push_back({mini[k],k});
mini[node] = min(mini[node],mini[k]);
}
}
sort(vect1.begin(),vect1.end());
adj[node].clear();
for(auto k:vect1){
adj[node].push_back(k.s);
}
}
int cnt = 1;
void dfs2(int node,int parent){
for(auto k:adj[node]){
if(k!=parent){
dfs2(k,node);
}
}
num[node] = cnt;
ipos[cnt] = node;
cnt++;
}
int find_parent(int a,int b){
for(int i=0;i<18;i++){
if(b&(1<<i)){
a = parents[i][a];
}
}
return a;
}
int32_t main(){
ios::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
int no_of_vertex,no_of_query;
int input1,input2;
cin >> no_of_vertex >> no_of_query;
int root = -1;
for(int i=1;i<=no_of_vertex;i++){
cin >> input1;
if(input1==0){
root = i;
}
else{
adj[i].push_back(input1);
adj[input1].push_back(i);
}
}
memset(parents,0,sizeof(parents));
dfs1(root,0);
for(int i=1;i<=17;i++){
for(int j=1;j<=no_of_vertex;j++){
parents[i][j] = parents[i-1][parents[i-1][j]];
}
}
dfs2(root,0);
set<int> nothave;
for(int i=1;i<=no_of_vertex;i++){
nothave.insert(i);
}
vector<int> has(maxn,0);
for(int i=0;i<no_of_query;i++){
cin >> input1 >> input2;
if(input1==1){//add
int lo = 0,hi = no_of_vertex+1;
while(lo+1!=hi){
int mid = (lo+hi)/2;
if(query(1,mid)+input2<=mid){
hi = mid;
}
else{
lo = mid;
}
}
//use hi
auto k = nothave.lower_bound(hi);
if(*k>hi){
k--;
}
cout << ipos[*k] << "\n";
for(int j=0;j<input2;j++){
int should = ipos[*k];
has[should] = 1;
add(*k);
if(j!=input2-1){
k--;
}
nothave.erase(num[should]);
}
}
else{//remove
int lo = 0,hi = no_of_vertex+1;
while(lo+1!=hi){
int mid = (lo+hi)/2;
int p = find_parent(input2,mid);
if(has[p]==0){
hi = mid;
}
else{
lo = mid;
}
}
/*cout << 0 << "\n";
has[input2] = 0;
nothave.insert(num[input2]);
add2(num[input2]);*/
cout << lo << "\n";
//assert(lo==0);
has[find_parent(input2,lo)] = 0;
nothave.insert(num[find_parent(input2,lo)]);
add2(num[find_parent(input2,lo)]);
}
}
}
