/**
* author: wxhtzdy
* created: 03.07.2022 19:51:50
**/
#include <bits/stdc++.h>
using namespace std;
template <typename T>
class fenwick {
public:
vector<T> fenw;
int n;
fenwick(int _n) : n(_n) {
fenw.resize(n);
}
void modify(int x, T v) {
while (x < n) {
fenw[x] += v;
x |= (x + 1);
}
}
T get(int x) {
T v{};
while (x >= 0) {
v += fenw[x];
x = (x & (x + 1)) - 1;
}
return v;
}
};
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, q;
cin >> n >> q;
vector<vector<int>> g(n);
int root;
for (int i = 0; i < n; i++) {
int p;
cin >> p;
--p;
if (p == -1) {
root = i;
} else {
g[p].push_back(i);
}
}
const int L = 20;
vector<vector<int>> jump(n, vector<int>(L));
vector<int> tin(n);
vector<int> tout(n);
vector<int> dep(n);
vector<int> mn(n);
int T = 0;
function<void(int, int)> Dfs = [&](int v, int pr) {
tin[v] = ++T;
dep[v] = dep[pr] + 1;
jump[v][0] = pr;
mn[v] = v;
for (int u : g[v]) {
Dfs(u, v);
mn[v] = min(mn[v], mn[u]);
}
tout[v] = ++T;
};
Dfs(root, root);
for (int i = 0; i < n; i++) {
sort(g[i].begin(), g[i].end(), [&](int x, int y) {
return mn[x] < mn[y];
});
}
vector<int> order(n);
T = 0;
Dfs = [&](int v, int pr) {
order[v] = ++T;
for (int u : g[v]) {
if (u != pr) {
Dfs(u, v);
}
}
};
Dfs(root, root);
for (int j = 1; j < L; j++) {
for (int i = 0; i < n; i++) {
jump[i][j] = jump[jump[i][j - 1]][j - 1];
}
}
vector<int> deg(n);
set<pair<int, int>> st;
for (int i = 0; i < n; i++) {
if (g[i].empty()) {
st.emplace(order[i], i);
}
}
fenwick<int> fenw(2 * (n + 1));
function<void(int, int)> Add = [&](int x, int v) {
fenw.modify(tin[x], v);
fenw.modify(tout[x], -v);
};
function<void(int)> Ins = [&](int x) {
deg[x] += 1;
if (deg[x] == (int) g[x].size()) {
st.emplace(order[x], x);
}
};
function<void(int)> Del = [&](int x) {
if (deg[x] == (int) g[x].size()) {
st.erase(st.find(make_pair(order[x], x)));
}
deg[x] -= 1;
};
while (q--) {
int op, x;
cin >> op >> x;
if (op == 1) {
int ans;
while (x--) {
auto it = st.begin();
int i = it->second;
st.erase(it);
Add(i, +1);
if (i != root) {
Ins(jump[i][0]);
}
ans = i;
}
cout << ans + 1 << '\n';
} else {
--x;
int cnt = fenw.get(tout[x]);
cout << cnt << '\n';
for (int i = L - 1; i >= 0; i--) {
if (cnt >> i & 1) {
x = jump[x][i];
}
}
Add(x, -1);
if (x != root) {
Del(jump[x][0]);
}
st.emplace(order[x], x);
}
}
return 0;
}
