#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define sz size()
#define ff first
#define ss second
#define pb push_back
#define pii pair <int, int>
#define dur exit(0)
#define dur1 return(0)
const int N = 2e5 + 5;
const int LOG = 17;
int qu[N], o, p[N][LOG], ball[N], val[N], bal[N];
set <pii> yok;
vector <int> v[N];
bool cmp (int x, int y) {
if (val[x] < val[y]) return 1;
return 0;
}
void dfs (int x, int par) {
val[x] = x;
for (int i : v[x]) {
if (i == par) continue;
dfs (i, x);
val[x] = min (val[x], val[i]);
}
sort (v[x].begin(), v[x].end(), cmp);
}
void dfs1 (int x, int par) {
for (int i : v[x]) {
if (i == par) continue;
dfs1 (i, x);
}
qu[++o] = x;
}
pii cykar (int x) {
int ret = 0;
for (int i = LOG - 1; i >= 0; i--) {
if (ball[p[x][i]]) {
x = p[x][i];
ret += (1 << i);
}
}
return {x, ret};
}
int main () {
// freopen ("input.txt", "r", stdin);
ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
int n, q, par;
cin >> n >> q;
for (int i = 1; i <= n; ++i) {
cin >> p[i][0];
if (p[i][0] != 0) {
v[p[i][0]].pb (i);
v[i].pb (p[i][0]);
}
else {
par = i;
}
}
dfs (par, -1);
dfs1 (par, -1);
for (int i = 1; i < LOG; ++i) {
for (int j = 1; j <= n; ++j) {
p[j][i] = p[p[j][i - 1]][i - 1];
}
}
for (int i = 1; i <= n; ++i) {
yok.insert ({i, qu[i]});
}
for (int i = 1; i <= n; ++i) {
bal[qu[i]] = i;
}
while ( q-- ) {
int type, x;
cin >> type >> x;
if (type == 1) {
int jog = -1;
for (int i = 1; i <= x; ++i) {
pii tr = *yok.begin();
yok.erase (yok.begin());
ball[tr.ss] = 1;
jog = tr.ss;
}
cout << jog << "\n";
}
else {
pii x1 = cykar (x);
cout << x1.ss << "\n";
ball[x1.ff] = 0;
yok.insert ({bal[x1.ff], x1.ff});
}
}
}
