#include <bits/stdc++.h>
using namespace std;
#define pb push_back
const int N=100050;
vector<int> E[N];
int sz[N],mn[N],hc[N];
void DFS(int u){
sz[u]=1;mn[u]=u;
for(int v:E[u])
DFS(v),
sz[u]+=sz[v],
mn[u]=min(mn[u],mn[v]),
hc[u]=sz[v]>sz[hc[u]]?v:hc[u];
}
int idx[N],isz;
void IDF(int u){
sort(E[u].begin(),E[u].end(),[&](int i,int j){return mn[i]<mn[j];});
for(int v:E[u])IDF(v);
idx[u]=++isz;
}
int lid[N],rid[N],nod[N],dep[N],tid,head[N];
void HLD(int u){
if(!head[u])head[u]=u;
for(int i=0;i<E[u].size();i++)if(E[u][i]==hc[u])swap(E[u][i],E[u][0]);
lid[u]=++tid;
nod[tid]=u;
if(hc[u])head[hc[u]]=head[u];
for(int v:E[u])dep[v]=dep[u]+1,HLD(v);
rid[u]=tid;
}
const int M=2*N;
int ls[M],rs[M],tsz,root,sum[M];
void Set(int &c,int ss,int se,int qi,int f){
if(!c)c=++tsz;
if(ss==se){sum[c]=f;return;}
int mid=ss+se>>1;
if(qi<=mid)Set(ls[c],ss,mid,qi,f);
else Set(rs[c],mid+1,se,qi,f);
sum[c]=sum[ls[c]]+sum[rs[c]];
}
int Search(int c,int ss,int se,int k){
if(ss==se)return sum[c]==k?ss:ss-1;
int mid=ss+se>>1;
if(sum[rs[c]]>=k)return Search(rs[c],mid+1,se,k);
else return Search(ls[c],ss,mid,k-sum[rs[c]]);
}
int Get(int c,int ss,int se,int qs,int qe){
if(qs>qe || qs>se || ss>qe)return 0;
if(qs<=ss && qe>=se)return sum[c];
int mid=ss+se>>1;
return Get(ls[c],ss,mid,qs,qe)+Get(rs[c],mid+1,se,qs,qe);
}
int Search(int ss,int se){return Search(root,1,N,Get(root,1,N,ss,N));}
int par[N];
int main(){
int n,q;
scanf("%i %i",&n,&q);
for(int i=1;i<=n;i++)scanf("%i",&par[i]),E[par[i]].pb(i);
int rt=E[0][0];
DFS(rt);
IDF(rt);
HLD(rt);
set<pair<int,int>> avb;
for(int i=1;i<=n;i++)avb.insert({idx[i],i});
while(q--){
int t,k;
scanf("%i %i",&t,&k);
if(t==1){
int las=-1;
while(k--){
auto p=*avb.begin();
avb.erase(p);
Set(root,1,N,lid[p.second],1);
las=p.second;
}
printf("%i\n",las);
}else{
int u=k,las=k,ans;
while(u){
int v=Search(lid[head[u]],lid[u]);
//printf("%i %i %i %i\n",head[u],u,nod[v],v);
if(v>lid[u]){ans=las;break;}
else if(v==lid[head[u]]){
las=head[u];
u=par[head[u]];
}else{ans=nod[v];break;}
}
if(u==0)ans=las;
//int ans=k;
//printf("ans: %i\n",ans);
printf("%i\n",dep[k]-dep[ans]);
avb.insert({idx[ans],ans});
Set(root,1,N,lid[ans],0);
}
}
return 0;
}
