#include <bits/stdc++.h>
using namespace std;
const int N = 100*1000+5;
int par[N];
vector<pair<int,int> > g[N];
int depth[N];
int d[N][25];
int sub[N];
void dfs(int v,int p = 0){
depth[v] = depth[p]+1;
d[v][0] = par[v];
sub[v] = v;
for(int i = 0;i<g[v].size();i++){
int to = g[v][i].second;
if(to == p) continue;
dfs(to,v);
sub[v] = min(sub[v],sub[to]);
g[v][i].first = sub[to];
}
sort(g[v].begin(),g[v].end());
}
pair<int,int> lca(int u,int v){
bool f = false;
if(depth[u]>depth[v]){
swap(u,v);
f = true;
}
int dif = depth[v]-depth[u];
for(int i = 0;i<=20;i++){
if((dif>>i)&1) v = d[v][i];
}
if(u == v) return {u,u};
// cout<<u<< " "<<v<<endl;
for(int i = 20;i>=0;i--){
if(d[u][i] == d[v][i]) continue;
u = d[u][i];
v = d[v][i];
}
if(f) swap(u,v);
return {u,v};
}
vector<int> all;
bool cmp(int u,int v){
pair<int,int> x = lca(u,v);
if(x.first == x.second) return depth[u]>depth[v];
return sub[x.first]<sub[x.second];
}
int hrt[N];
bool used[N];
void go(int v,int p = -1){
for(int i = 0;i<g[v].size();i++){
int to = g[v][i].second;
if(to == p) continue;
go(to,v);
}
/*for(int i = 0;i<all.size();i++){
if(all[i] == v) return;
}*/
all.push_back(v);
}
int main(){
ios_base::sync_with_stdio(false);
int n,q;
cin>>n>>q;
int root;
for(int i = 1;i<=n;i++){
int x;
cin>>x;
if(!x) x = -1;
par[i] = x;
if(x == -1) {
root = i;
continue;
}
g[i].push_back({0,x});
g[x].push_back({0,i});
}
memset(d,-1,sizeof(d));
dfs(root);
for(int k = 1;k<=20;k++){
for(int i = 1;i<=n;i++){
if(d[i][k-1]!=-1){
d[i][k] = d[d[i][k-1]][k-1];
}
}
}
all.clear();
// go(root);
// cout<<all.size()<<endl;
/*for(int i = 0;i<all.size();i++){
if(all[i]>=1 && all[i]<=n) continue;
cout<<"yyyy "<<all[i]<<endl;
}*/
// system("pause");
for(int i = 1;i<=n;i++) all.push_back(i);
sort(all.begin(),all.end(),cmp);
//for(int i = 0;i<all.size();i++) cout<<all[i]<<" ";
//cout<<endl;
priority_queue<pair<int,int> > pq;
for(int i = 0;i<all.size();i++){
pq.push({-i,all[i]});
hrt[all[i]] = i;
}
/*int x,y;
while(cin>>x>>y){
pair<int,int> w = lca(x,y);
cout<<w.first<<" "<<w.second<<endl;
}*/
memset(used,0,sizeof(used));
while(q--){
int tp;
cin>>tp;
if(tp == 1){
int k;
cin>>k;
/*if(k>ms.size()){
cout<<k<< " "<<ms.size()<<endl;
system("pause");
}*/
// k = min(k,(int)ms.size());
while(k--){
pair<int,int> x = pq.top();
pq.pop();
used[x.second] = 1;
if(!k){
cout<<x.second<<endl;
}
}
}
else{
int x;
cin>>x;
int nax = x;
int ans = 0;
for(int i = 20;i>=0;i--){
int u = d[x][i];
if(u == -1) continue;
if(!used[u]) continue;
x = d[x][i];
}
used[x] = 0;
pq.push({-hrt[x],x});
ans = depth[nax]-depth[x];
cout<<ans<<endl;
}
}
return 0;
}
