#include<bits/stdc++.h>
#define str string
#define task "strdel"
#define ii pair<int,int>
#define iii pair<int,ii>
#define iv pair<ii,ii>
#define se second
#define fi first
#define ffi fi.fi
#define sfi se.fi
#define sse se.se
#define fse fi.se
#define lt(i, c, d) for(int i = c; i <= d; ++i)
#define fl(i, c, d) for(int i = d; i >= c; --i)
#define pb push_back
#define emb emplace_back
#define emf emplace_front
#define em emplace
using namespace std;
const int N=1e5+5,lg=20,mod=1e9+7;
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
int Rand(int u,int v){
return u+rd()%(v-u+1);
}
int n,q,goc,sz[N],h[N],zz,M[N],up[N][lg+5],minn[N];
vector<int>a[N];
bool k[N];
vector<int>res1;
void dfs1(int u){
for(int v:a[u]){
dfs1(v);
}
res1.emb(u);
}
set<ii>s;
void dfs(int u){
minn[u]=u;sz[u]=1;
for(int v:a[u]){
h[v]=h[u]+1;
up[v][0]=u;
dfs(v);
minn[u]=min(minn[u],minn[v]);
}
}
void giai1(int x){
while(x--){
k[(*s.begin()).se]=1;zz=(*s.begin()).se;
s.erase(s.begin());
}
cout <<zz<<'\n';
}
int laycha(int x,int u){
for(int j=0;j<=lg;++j){
if(u&(1<<j)){
x=up[x][j];
}
}
return x;
}
void giai2(int x){
int l=1,r=h[x],res=0;
while(l<=r){
int mid=(r+l)>>1;
int u=laycha(x,mid);
// cout <<u<<" "<<k[u]<<'\n';
if(!k[u]){
r=mid-1;
}
else{
l=mid+1;
res=mid;
}
}
// cout <<res;
int u=laycha(x,res);
k[u]=false;
s.insert({M[u],u});
cout <<res<<'\n';
}
void solve(){
cin >> n >> q;
for(int i=1;i<=n;++i){
int u;
cin >> u;
if(u==0)goc=i;
else a[u].emb(i);
}
dfs(goc);
for(int j=1;j<=lg;++j)
for(int i=1;i<=n;++i)up[i][j]=up[up[i][j-1]][j-1];
for(int i=1;i<=n;++i){
sort(a[i].begin(),a[i].end(),[](const int &x,const int &y){
return minn[x]<minn[y];
});
}
dfs1(goc);
for(int i=1;i<=n;++i){
s.insert({i,res1[i-1]});
M[res1[i-1]]=i;
}
while(q--){
int t,u;
cin >> t >> u;
if(t==1)giai1(u);
else giai2(u);
}
}
main()
{
srand(time(0));
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
if(fopen(task".inp","r")){
freopen(task".inp","r",stdin);
freopen(task".out","w",stdout);
}
int t=1;
// cin >> t;
while(t--){
solve();
}
}
