#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int inf = 1e9 + 7;
const ll infll = 1e18;
template<typename T>
istream &operator>>(istream &is, vector<T> &a) {
for (auto &i : a) {
is >> i;
}
return is;
}
struct BinaryJumps {
static const int lg = 17;
vector<int> d;
vector<vector<int>> up;
BinaryJumps() {}
BinaryJumps(int n) {
d.resize(n);
up.resize(lg, vector<int>(n, -1));
}
void add_leaf(int v, int p) {
d[v] = d[p] + 1;
up[0][v] = p;
for (int i = 1; i < lg; ++i) {
if (up[i - 1][v] != -1) {
up[i][v] = up[i - 1][up[i - 1][v]];
}
}
}
pair<int, int> la(int v, const function<bool(int)> &f) {
int u = v;
for (int i = lg - 1; i >= 0; --i) {
if (up[i][u] == -1) {
continue;
}
if (f(up[i][u])) {
u = up[i][u];
}
}
return {u, d[v] - d[u]};
}
};
vector<vector<int>> g;
BinaryJumps tr;
vector<int> mn;
vector<int> tin, tout;
int timer = 0;
void dfs1(int v, int p = -1) {
mn[v] = v;
for (auto u : g[v]) {
if (u != p) {
dfs1(u, v);
mn[v] = min(mn[v], mn[u]);
}
}
}
void dfs2(int v, int p = -1) {
tin[v] = timer++;
vector<int> ch;
for (auto u : g[v]) {
if (u != p) {
ch.push_back(u);
}
}
sort(ch.begin(), ch.end(), [&](int a, int b) {
return mn[a] < mn[b];
});
for (auto u : ch) {
tr.add_leaf(u, v);
dfs2(u, v);
}
tout[v] = timer++;
}
int32_t main() {
#ifdef LOCAL
freopen("/tmp/input.txt", "r", stdin);
#else
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
int n, q;
cin >> n >> q;
g.resize(n);
int root = -1;
for (int i = 0; i < n; ++i) {
int p;
cin >> p;
--p;
if (p == -1) {
root = i;
} else {
g[p].push_back(i);
g[i].push_back(p);
}
}
mn.resize(n);
dfs1(0);
tr = BinaryJumps(n);
tin.resize(n);
tout.resize(n);
dfs2(0);
vector<bool> mark(n);
set<pair<int, int>> st;
for (int i = 0; i < n; ++i) {
st.insert({tout[i], i});
}
while (q--) {
int t;
cin >> t;
if (t == 1) {
int k;
cin >> k;
int last = -1;
while (k > 0) {
auto [_, v] = *st.begin();
st.erase(st.begin());
last = v;
mark[v] = 1;
--k;
}
cout << last + 1 << "\n";
} else {
int v;
cin >> v;
--v;
auto [u, d] = tr.la(v, [&](int v) {
return mark[v];
});
mark[u] = 0;
st.insert({tout[u], u});
cout << d << "\n";
}
}
return 0;
}
