/* IN THE NAME OF GOD */
// Oh, let the bullets fly, oh, let them rain
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 100'000, lg = 18;
bool is_filled[MAXN + 10];
int par_sp[MAXN + 10][lg + 10], order[MAXN + 10], mn[MAXN + 10], par[MAXN + 10], n, q, tt;
vector<int> adj[MAXN + 10];
set<pair<int, int>> take_order;
void input();
void solve();
void dfs_get_minimum(int u, int par);
void dfs_get_order(int u, int par);
void par_spars_table();
int query1(int cnt);
int query2(int id);
int main() {
ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
input();
solve();
return 0;
}
void input() {
cin >> n >> q;
for (int i = 0; i < n; i++) {
cin >> par[i];
par[i]--;
if (par[i] == -1)
continue;
adj[par[i]].push_back(i);
adj[i].push_back(par[i]);
}
}
void solve() {
dfs_get_minimum(0, -1);
dfs_get_order(0, -1);
par_spars_table();
//cout << par_sp[7][2] << '\n';
for (int i = 0; i < n; i++)
take_order.insert({order[i], i});
while (q--) {
int type, x;
cin >> type >> x;
if (type == 1)
cout << query1(x) + 1 << '\n';
else {
x--;
cout << query2(x) << '\n';
}
}
}
void dfs_get_minimum(int u, int par) {
int res = u;
for (int v : adj[u])
if (v != par) {
dfs_get_minimum(v, u);
res = min(res, mn[v]);
}
mn[u] = res;
}
void dfs_get_order(int u, int par) {
set<pair<int, int>> st;
for (int v : adj[u])
if (v != par)
st.insert({mn[v], v});
for (auto p : st)
dfs_get_order(p.second, u);
order[u] = tt++;
}
void par_spars_table() {
for (int i = 0; i < n; i++)
par_sp[i][0] = par[i];
for (int k = 1; k < lg; k++)
for (int i = 0; i < n; i++) {
if (par_sp[i][k - 1] == -1)
par_sp[i][k] = -1;
else
par_sp[i][k] = par_sp[par_sp[i][k - 1]][k - 1];
}
}
int query1(int cnt) {
for (int i = 0; i < cnt; i++) {
int u = (*take_order.begin()).second;
is_filled[u] = true;
take_order.erase(take_order.begin());
if (i == cnt - 1)
return u;
}
}
int query2(int id) {
int u = id, ans = 0;
for (int k = lg - 1; k >= 0; k--) {
if (par_sp[u][k] == -1)
continue;
if (is_filled[par_sp[u][k]] == true) {
u = par_sp[u][k];
ans += (1 << k);
}
}
is_filled[u] = false;
take_order.insert({order[u], u});
return ans;
}
