#include<bits/stdc++.h>
#define ll long long
#define ss second
#define ff first
#define pb push_back
#define endl "\n"
using namespace std;
ll n,q,rr,a[100005];
set<pair<ll,ll> > s;
vector<vector<ll> > v,sp;
vector<ll> m,v1,b,vv;
void rec(ll x,ll y){
m[x]=x;
for(auto i:v[x])
{if(i==y) continue;
rec(i,x);
m[x]=min(m[x],m[i]);
}
}
void res(ll x,ll y){
vector<pair<ll,ll> > v2;
for(auto i:v[x])
{if(i==y) continue;
v2.pb({m[i],i});
}
sort(v2.begin(),v2.end());
for(ll i=0; i<v2.size(); i++)
{res(v2[i].ss,x);
}
v1.pb(x);
}
ll rev(ll x){
ll c=0;
for(ll i=20; i>=0; i--)
{ll k=sp[x][i];
if(vv[k]==1){x=k; c+=(1<<i);}
}
cout<<c<<endl;
return x;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin>>n>>q;rr=1;
v.resize(n+1);
m.resize(n+1);
sp.resize(n+1,vector<ll> (25));
for(ll i=1; i<=n; i++)
{cin>>a[i];
sp[i][0]=a[i];
if(a[i]==0) rr=i;
else{v[a[i]].pb(i);v[i].pb(a[i]);}
}
rec(rr,0);
res(rr,0);
b.resize(n+1);
vv.resize(n+1,0);
for(ll i=0; i<v1.size(); i++)
{s.insert({i,v1[i]});
b[v1[i]]=i;
}
for(ll j=1; j<=20; j++)
{
for(ll i=1; i<=n; i++)
{sp[i][j]=sp[sp[i][j-1]][j-1];
}
}
while(q--){ll k,t,x;
cin>>t>>x;
if(t==1){
while(x--){
k=(*s.begin()).ss;
vv[k]=1;
s.erase(s.begin());
}
cout<<k<<endl;
}
else{
k=rev(x);
vv[k]=0;
s.insert({b[k],k});
}
}
}
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