#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],up[N][lg+5],minn[N];
int st[N*4],lazy[N*4];
vector<int>a[N];
void down(int id){
st[id<<1]+=lazy[id];
st[id<<1|1]+=lazy[id];
lazy[id<<1|1]+=lazy[id];
lazy[id<<1]+=lazy[id];
lazy[id]=0;
}
int walk_up(int id,int r,int l,int u,int v,int val)
{
if(r<u||l>v||st[id]>val)
return -1;
if(l==r)
{
return r;
}
down(id);
int mid=(l+r)>>1;
int res=walk_up(id<<1|1,mid+1,l,u,v,val);
if (res==-1)
res=walk_up(id<<1,r,mid,u,v,val);
return res;
}
int walk_down(int id,int l,int r,int u,int v,int val)
{
if(r<u||l>v||st[id]>val)
return -1;
if(l==r)
{
return r;
}
down(id);
int mid=(l+r)>>1;
int res=walk_down(id<<1,r,mid,u,v,val);
if (res==-1)
res=walk_down(id<<1|1,mid+1,l,u,v,val);
return res;
}
void update(int id,int r,int l,int u,int v,int val){
if(r>v||l<u)return;
if(r>=u&l<=v){
st[id]+=val;
lazy[id]+=val;
return;
}
int mid=(r+l)>>1;
down(id);
update(id<<1,r,mid,u,v,val);
update(id<<1|1,mid+1,l,u,v,val);
st[id]=st[id<<1]+st[id<<1|1];
}
int get(int id,int r,int l,int u,int v){
if(r>v||l<u)return 0;
if(r>=u&&l<=v)return st[id];
int mid=(r+l)>>1;
down(id);
return get(id<<1,r,mid,u,v)+get(id<<1|1,mid+1,l,u,v);
}
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);
sz[u]+=sz[v];
minn[u]=min(minn[u],minn[v]);
}
}
int arr[N],curid[N],curhead[N],pos[N],curc=1,curpos=1;
void hld(int u,int cha){
// cout <<u<<" ";
if(!curhead[curc]){
curhead[curc]=u;
}
curid[u]=curc;
pos[u]=curpos;
arr[curpos]=u;
curpos++;
int nxt=0;
for(int v:a[u]){
if(v!=cha){
if(sz[nxt]<sz[v])nxt=v;
}
}
if(nxt)hld(nxt,u);
for(int v:a[u]){
if(v!=nxt&&v!=cha){
++curc;
hld(v,u);}
}
}
int lca(int u,int v){
while(curid[u]!=curid[v]){
if(curid[u]>curid[v]){
u=up[curhead[curid[u]]][0];
}
else{
v=up[curhead[curid[v]]][0];
}
}
// cout <<u<<" "<<v<<'\n';
if(h[u]<h[v])return u;
return v;
}
long long query(int u,int v){
long long ans=0,l=lca(u,v);
while(curid[u]!=curid[l]){
ans+=get(1,1,n,pos[curhead[curid[u]]],pos[u]);
u=up[curhead[curid[u]]][0];
}
while(curid[v]!=curid[l]){
ans+=get(1,1,n,pos[curhead[curid[v]]],pos[v]);
v=up[curhead[curid[v]]][0];
}
if(h[u]<h[v]){
ans+=get(1,1,n,pos[u],pos[v]);
}
else ans+=get(1,1,n,pos[v],pos[u]);
return ans;
}
int sl,zz;
void dfs1(int u){
for(int v:a[u]){
if(query(v,v)==0)
dfs1(v);
}
if(sl>0&&query(u,u)==0){
zz=u;
sl--;
update(1,1,n,pos[u],pos[u],1);
}
}
void giai1(int x){
sl=x;
dfs1(goc);
// cout <<query(1,7);
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);
int sum=query(u,x);
if(sum!=h[x]-h[u]+1){
r=mid-1;
}
else{
l=mid+1;
res=mid;
}
}
int
u=laycha(x,res);
// cout <<u<<" "<<res;
update(1,1,n,pos[u],pos[u],-1);
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);
hld(goc,-1);
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];
});
}
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();
}
}
