/// dwuy: _,\,,,_\,__,\,,_
#include <bits/stdc++.h>
#define fastIO ios_base::sync_with_stdio(false); cin.tie(NULL)
#define file(a) freopen(a".inp","r",stdin); freopen(a".out", "w",stdout)
#define fi first
#define se second
#define endl "\n"
#define len(s) int32_t(s.length())
#define MASK(k)(1LL<<(k))
#define TASK ""
using namespace std;
typedef tuple<int, int, int> tpiii;
typedef pair<double, double> pdd;
typedef pair<int, int> pii;
typedef long long ll;
const long long OO = 1e18;
const int MOD = 1e9 + 7;
const int INF = 1e9;
struct SMT{
int n;
vector<int> tree;
SMT(int n=0){
this->n = n;
this->tree.assign(n<<2|1, 0);
}
void down(int id){
if(tree[id]==0) return;
tree[id<<1] += tree[id];
tree[id<<1|1] += tree[id];
tree[id] = 0;
}
void update(int l, int r, int id, const int &u, const int &v, const int &val){
if(l>v || r<u) return;
if(l>=u && r<=v){
tree[id] += val;
return;
}
down(id);
int mid = (l+r)>>1;
update(l, mid, id<<1, u, v, val);
update(mid+1, r, id<<1|1, u, v, val);
}
void update(int l, int r, int val){
update(1, n, 1, l, r, val);
}
int get(int pos){
int id = 1;
for(int lo=1, hi=n; lo<hi;){
down(id);
int mid = (lo+hi)>>1;
if(pos<=mid) id = id<<1, hi = mid;
else lo = mid + 1, id = id<<1|1;
}
return tree[id];
}
};
const int MX = 100005;
int n, q;
vector<int> G[MX];
void nhap(){
cin >> n >> q;
for(int i=1; i<=n; i++){
int u; cin >> u;
G[u].push_back(i);
}
}
int p[MX][17];
int num[MX];
int clo[MX];
int mnID[MX];
int dfsID = 0;
void calcID(int u){
mnID[u] = u;
for(int v: G[u]){
calcID(v);
p[v][0] = u;
mnID[u] = min(mnID[u], mnID[v]);
}
}
bool comp(const int &a, const int &b){
return mnID[a] < mnID[b];
}
void dfs(int u){
num[u] = ++dfsID;
sort(G[u].begin(), G[u].end(), comp);
for(int v: G[u]) dfs(v);
clo[u] = dfsID;
}
int cnt[MX];
void solve(){
int root = G[0][0];
calcID(root);
dfs(root);
set<pair<int, int>> Q;
for(int i=1; i<=n; i++) if(G[i].size() == 0){
Q.insert({num[i], i});
}
for(int j=1; j<=16; j++){
for(int i=1; i<=n; i++){
p[i][j] = p[p[i][j-1]][j-1];
}
}
SMT smt(n);
while(q--){
int oper, u;
cin >> oper >> u;
if(oper == 1){
int ans = 0;
while(u--){
int v = Q.begin()->se; Q.erase(Q.begin());
ans = v;
smt.update(num[v], clo[v], 1);
if(++cnt[p[v][0]] == (int)G[p[v][0]].size()){
Q.insert({num[p[v][0]], p[v][0]});
}
}
cout << ans << endl;
}
if(oper == 2){
int h = smt.get(num[u]) - 1;
int v = u;
for(int t=h; t; t-=-t&t) v = p[v][__lg(-t&t)];
smt.update(num[v], clo[v], -1);
if(cnt[p[v][0]] == (int)G[p[v][0]].size()){
Q.erase(Q.find({num[p[v][0]], p[v][0]}));
}
cnt[p[v][0]]--;
Q.insert({num[v], v});
cout << h << endl;
}
}
}
int32_t main(){
fastIO;
//file(TASK);
nhap();
solve();
return 0;
}
