#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
// #include "temp.cpp"
#include <cstdio>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; print(x); cerr << endl;
#else
#define dbg(x)
#endif
#define sz(x) (int((x).size()))
#define len(x) (int)x.length()
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define clr(x) x.clear()
#define uniq(x) x.resize(unique(all(x)) - x.begin());
#define blt __builtin_popcount
#define pb push_back
#define pf push_front
#define popf pop_front
#define popb pop_back
void print(long long t) {cerr << t;}
void print(int t) {cerr << t;}
void print(string t) {cerr << t;}
void print(char t) {cerr << t;}
void print(double t) {cerr << t;}
void print(long double t) {cerr << t;}
void print(unsigned long long t) {cerr << t;}
template <class T> void print(set <T> v);
template <class T> void print(vector <T> v);
template <class T> void print(multiset <T> v);
template <class T, class V> void print(map <T, V> v);
template <class T, class V> void print(pair <T, V> p);
template <class T, class V> void print(T v[],V n) {cerr << "["; for(int i = 0; i < n; i++) {print(v[i]); cerr << " "; } cerr << "]";}
template <class T, class V> void print(pair <T, V> p) {cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}";}
template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(deque<T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(set <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(multiset <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void print(map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void print(unordered_map<T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]";}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define nl '\n'
// for grid problems
int dx[8] = {-1,0,1,0,1,-1,1,-1};
int dy[8] = {0,1,0,-1,1,1,-1,-1};
// lowest / (1 << 17) >= 1e5 / (1 << 18) >= 2e5 / (1 << 21) >= 1e6
void fastIO() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);
}
// file in/out
void setIO(string str = "") {
fastIO();
if (str != "" && str != "input") {
freopen((str + ".in").c_str(), "r", stdin);
freopen((str + ".out").c_str(), "w", stdout);
}
if(str == "input") {
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
}
}
// Indexed Set
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const int N = 1e5 + 10, inf = 1e9, LOG = 22;
int n, q, root = -1, mini[N], sit[N], up[N][LOG];
vector<int> adj[N], order;
set<pair<int, int>> st;
int dfsMin(int node, int parent) {
mini[node] = node;
for(auto u: adj[node]) {
if(u == parent) continue;
up[u][0] = node;
for(int i = 1; i < LOG; i++) {
up[u][i] = up[up[u][i - 1]][i - 1];
}
mini[node] = min(mini[node], dfsMin(u, node));
}
return mini[node];
}
void dfsOrder(int node, int parent) {
vector<pair<int, int>> children;
for(auto u: adj[node]) {
if(u == parent) continue;
children.emplace_back(mini[u], u);
}
sort(all(children));
for(auto u: children) {
dfsOrder(u.second, node);
}
order.push_back(node);
}
pair<int, int> findAncestor(int node) {
int answ = 0;
for(int i = LOG - 1; i >= 0; i--) {
if(up[node][i] && st.find({sit[up[node][i]], up[node][i]}) == st.end()) {
node = up[node][i];
answ |= (1 << i);
}
}
return {node, answ};
}
void solve_() {
cin >> n >> q;
for(int i = 1; i <= n; i++) {
int parent; cin >> parent;
if(!parent) {
root = i;
continue;
}
adj[i].push_back(parent);
adj[parent].push_back(i);
mini[i] = inf;
}
dfsMin(root, root);
dfsOrder(root, root);
// seg.upd(0, 1, 1);
for(int i = 0; i < n; i++) {
sit[order[i]] = i + 1;
st.insert({i + 1, order[i]});
}
while(q--) {
int type, a; cin >> type >> a;
if(type == 1) {
int lst = -1;
while(a--) {
lst = st.begin()->second;
st.erase(st.begin());
}
printf("%d\n", lst);
} else {
auto ans = findAncestor(a);
st.insert({sit[ans.first], ans.first});
printf("%d\n", ans.second);
}
}
}
int main() {
setIO();
auto solve = [&](int test_case)-> void {
while(test_case--) {
solve_();
}
};
int test_cases = 1;
solve(test_cases);
return 0;
}
