#include <bits/stdc++.h>
#define N 100005
#define ll long long int
#define fo(i,x,y) for(int i=x;i<=y;i++)
#define fs(ar,n) fo(i,1,n) cin>>ar[i]
#define sp " "
#define fast cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(false)
#define pb push_back
#define ppb pop_back
#define fi first
#define se second
#define ii pair<int,int>
#define lli pair<ll,ll>
#define fast2 freopen ("in.txt","r",stdin);freopen ("out.txt","w",stdout);
#define mod 1000000007
using namespace std;
ll n,m,ar[N],sum,t,tut1[N],cnt,tut[N],dad[N][19],mark[N],deg[N];
vector<int> v[N];
bool cmp(int a,int b)
{
return tut1[a]<tut1[b];
}
void f1(int ind,int back,int dg)
{
ll mn=ind;
deg[ind]=dg;
dad[ind][0]=back;
for(int i=1;i<=17;i++)
dad[ind][i]=dad[dad[ind][i-1]][i-1];
for(int i=0;i<v[ind].size();i++)
{
ll x=v[ind][i];
if(x!=back)
f1(x,ind,dg+1);
mn=min(mn,tut1[x]);
}
tut1[ind]=mn;
return;
}
void f(int ind,int back)
{
for(int i=0;i<v[ind].size();i++)
{
ll x=v[ind][i];
if(x!=back)
f(x,ind);
}
tut[ind]=++cnt;
}
struct node{
int a;
};
bool operator<(node a,node b)
{
return tut[a.a]>tut[b.a];
}
priority_queue<node> pq;
ll f2(int ind)
{
for(int i=18;i>=0;i--)
if(mark[dad[ind][i]])
ind=dad[ind][i];
return ind;
}
int main()
{
fast;
cin>>n>>m;
int rt=1;
fo(i,1,n)
{
ll a;
cin>>a;
if(a==0)
rt=i;
v[a].pb(i);
}
f1(rt,0,0);
fo(i,1,n)
sort(v[i].begin(),v[i].end(),cmp);
f(rt,0);
ll top=0;
fo(i,1,n)
{
node tt;
tt.a=i;
pq.push(tt);
}
fo(i,1,m)
{
int a,b;
cin>>a>>b;
if(a==1)
{
ll x=0;
fo(i,1,b)
{
x=pq.top().a;
pq.pop();
mark[x]=1;
}
cout<<x<<endl;
}
else
{
ll x=f2(b);
ll y=deg[b]-deg[x];
node tt;
tt.a=x;
pq.push({tt});
mark[x]=0;
cout<<y<<endl;
}
}
// cout<<tut1[i]<<sp;
}
