#include <bits/stdc++.h>
#define loop(a, b) for(int a = 0; a < b; ++a)
#define loop1(a, b) for(int a = 1; a <= b; ++a)
#define loopc(a, c, b) for(int a = c; a < b; ++a)
#define loopr(a, b) for(int a = b-1; a >= 0; --a)
#define mp make_pair
using namespace std;
typedef priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > pair_queue;
int nn, qq, q, v;
vector<int> tree[100001];
int par[20][100001], sub[100001];
map<int, int> order;
pair_queue que;
bool val[100001];
void dfsdep(int n) {
int s = n;
loop(a, tree[n].size()) {
dfsdep(tree[n][a]);
s = min(s, sub[tree[n][a]]);
}
sub[n] = s;
}
bool ord(const int &a, const int &b) {
return sub[a] < sub[b];
}
void dfsord(int n) {
sort(tree[n].begin(), tree[n].end(), ord);
loop(a, tree[n].size()) {
dfsord(tree[n][a]);
}
order[n] = que.size();
que.push(mp(order[n], n));
}
int main() {
cin >> nn >> qq;
loop1(a, nn) {
cin >> par[0][a];
tree[par[0][a]].push_back(a);
}
loop1(a, 18) {
loop1(b, nn) {
par[a][b] = par[a-1][par[a-1][b]];
}
}
/*loop(a, 18) {
loop1(b, nn) {
cout << par[a][b] << " " ;
}
cout << endl;
}*/
dfsdep(0);
dfsord(0);
/*loop1(a, nn) {
cout << sub[a] << " ";
}
cout << endl;*/
pair<int, int> vv;
int dd, pp;
loop(w, qq) {
cin >> q >> v;
if (q==1) {
while (v--) {
vv = que.top();
val[vv.second] = true;
que.pop();
}
cout << vv.second << endl;
}
else if (q==2) {
pp = v;
dd = 0;
loopr(a, 18) {
//cout <<pp << " " << dd << " " << a << endl;
//cout << par[a][pp] << endl << endl;;
if (val[par[a][pp]]) {
pp = par[a][pp];
dd += 1<<a;
}
}
val[pp] = false;
que.push(mp(order[pp], pp));
//cout <<pp << " " << dd << endl;
cout << dd << endl;
}
/*loop1(a, nn) {
cout << val[a] << " ";
}
cout << endl;*/
}
return 0;
}
