#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<ll>;
using pl = pair<ll,ll>;
#define pb push_back
#define form(m,it) for(auto it=m.begin(); it!=m.end(); it++)
#define forp(i,a,b) for(ll i=a; i<=b; i++)
#define forn(i,a,b) for(ll i=a; i>=b; i--)
#define newl '\n'
#define ff first
#define ss second
const ll mod = 998244353;
const ll maxn = 1e5 + 5;
ll lgn;
ll up[maxn][20];
vi adj[maxn];
ll occur[maxn];
bool col[maxn];
vi euler;
ll sub[maxn];
ll depth[maxn];
void order(ll i, ll pa){
sub[i]=i;
for(auto u:adj[i]){
if(u!=pa){
order(u,i);
sub[i]=min(sub[i],sub[u]);
}
}
}
void dfs(ll i, ll pa){
up[i][0]=pa;
forp(j,1,lgn){
up[i][j]=up[up[i][j-1]][j-1];
}
for(auto u:adj[i]){
if(u!=pa){
depth[u]=depth[i]+1;
dfs(u,i);
}
}
euler.pb(i);
occur[i]=euler.size();
}
ll find_anc(ll u, ll k){
ll ind=0;
while(k>0){
if(k%2==1){
u=up[u][ind];
}
ind++;
k/=2;
}
return u;
}
void solve(){
ll n,q; cin>>n>>q;
ll root; lgn=ceil(log2(n));
forp(i,1,n){
ll p; cin>>p;
if(p==0){
root=i;
} else {
adj[i].pb(p);
adj[p].pb(i);
}
}
order(root,0);
forp(i,1,n){
sort(adj[i].begin(), adj[i].end(), [](ll u, ll v){
return sub[u]<sub[v];
});
}
dfs(root,root);
set<pl> s;
forp(i,1,n){
s.insert({occur[i],i});
}
forp(i,1,q){
ll t,x; cin>>t>>x;
if(t==1){
pl node;
while(x--){
node = *s.begin();
col[node.ss]=1;
s.erase(s.begin());
}
cout<<node.ss<<newl;
} else {
ll l=0,r=depth[x];
while(l<r){
ll mid=(l+r+1)>>1;
if(col[find_anc(x,mid)]){
l=mid;
} else {
r=mid-1;
}
}
ll ans=find_anc(x,l);
cout<<depth[x]-depth[ans]<<newl;
col[ans]=0;
s.insert({occur[ans],ans});
}
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t=1; //cin>>t;
while(t--)solve();
}
