#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int> pii;
int n,m,p[100001][18],mmin[100001],root,dis[100001],pos[100001];
vector<int> adj[100001],ord;
priority_queue<pii, vector<pii>, greater<pii>> q;
bool emp[100001]; //less than cnt and empty (also in q)
int dfs(int x, int par) {
mmin[x]=x;
dis[x]=dis[par]+1;
for (auto s : adj[x]) {
if (s==par) continue;
mmin[x]=min(mmin[x],dfs(s,x));
}
return mmin[x];
}
void dfs_ord(int x, int par) {
vector<pii> v;
for (auto s : adj[x]) {
if (s==par) continue;
v.push_back(pii(mmin[s],s));
}
sort(v.begin(),v.end());
for (auto s : v) dfs_ord(s.second,x);
ord.push_back(x);
}
void dfs_par(int x, int par) {
for (int i=1; i<=17; ++i) p[x][i]=p[p[x][i-1]][i-1];
for (auto s : adj[x]) {
if (s==par) continue;
dfs_par(s,x);
}
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
cin>>n>>m;
for (int i=1; i<=n; ++i) {
int x; cin>>x;
p[i][0]=x;
adj[x].push_back(i);
if (x==0) root=x;
}
dfs(root,root);
dfs_ord(root,root);
dfs_par(root,root);
for (int i=0; i<n; ++i) pos[ord[i]]=i;
pos[0]=100010;
int cnt=-1;
while (m--) {
int mode,x; cin>>mode>>x;
if (mode==1) {
int ans=-1;
while (!q.empty() && x) {
--x;
ans=ord[q.top().second];
emp[q.top().second]=false;
q.pop();
}
cnt+=x;
if (x) cout<<ord[cnt]<<"\n";
else cout<<ans<<"\n";
} else {
int y=x;
for (int i=17; i>=0; --i) if (!emp[pos[p[x][i]]] && pos[p[x][i]]<=cnt) x=p[x][i];
cout<<dis[y]-dis[x]<<"\n";
emp[pos[x]]=true;
q.push(pii(mmin[x],pos[x]));
}
}
}
