//----------vahagng----------//
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
using namespace std;
// using namespace __gnu_pbds;
// template <class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; print(x); cerr << endl;
#else
#define dbg(x)
#endif
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, class V> void print(pair <T, V> p);
template <class T> void print(vector <T> v);
template <class T> void print(set <T> v);
template <class T, class V> void print(map <T, V> v);
template <class T> void print(multiset <T> v);
template <class T, class V> void print(T v[], V n) { cerr << "["; for (int i = 0; i < n; i++) { cerr << v[i] << " "; } 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(set <T> v) { cerr << "[ "; for (T i : v) { print(i); cerr << " "; } cerr << "]"; }
template <class T> void print(unordered_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 << "]"; }
#define ll long long
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define ld long double
#define sz(v) v.size()
#define endl '\n'
const ll inf = 2e18, mod = 1e9 + 7, mod2 = 998244353;
void SetIO(string str = "") {
if (str != "") {
freopen((str + ".in").c_str(), "r", stdin);
freopen((str + ".out").c_str(), "w", stdout);
}
else {
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
}
}
void FastIO() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
}
const int N = 3e5 + 10, M = 2e7 + 10;
mt19937 rnd(chrono::system_clock::now().time_since_epoch().count());
ll binpow(ll a, ll b, ll m) {
ll res = 1;
while (b) {
if (b & 1) {
res = (res * a) % m;
}
b >>= 1;
a = (a * a) % m;
}
return res;
}
ll n, q, mn[N], dp[N], up[N][20], ind[N];
vector<int>adj[N], ord[N], tout;
bool ka[N];
void dfs(int node, int parent) {
mn[node] = node;
for (auto i : adj[node]) {
if (i == parent) continue;
dfs(i, node);
mn[node] = min(mn[i], mn[node]);
}
vector<pair<int, int>> cur;
for(auto i : adj[node]){
if (i == parent) continue;
cur.push_back({ mn[i], i });
}
sort(all(cur));
for (auto i : cur) {
ord[node].push_back(i.second);
}
}
void dfs0(int node, int parent) {
dp[node] = dp[parent] + 1;
up[node][0] = parent;
for(int i = 1; i < 20; i++){
up[node][i] = up[up[node][i - 1]][i - 1];
}
for (auto i : ord[node]) {
if (i == parent) continue;
dfs0(i, node);
}
tout.push_back(node);
}
void solve(int tc) {
cin >> n >> q;
int r = 0;
for (int i = 1; i <= n; i++) {
int p;
cin >> p;
if(!p){
r = i;
}
else {
adj[p].push_back(i);
adj[i].push_back(p);
}
}
dfs(r, 0);
dfs0(r, 0);
set<pair<int, int>> st1, st2;
for (int i = 1; i <= n; i++) {
ind[tout[i - 1]] = i;
st1.insert({ i, tout[i - 1] });
}
// dbg(st1);
while (q--) {
int type, k;
cin >> type >> k;
if (type == 1) {
int ans = -1;
while (k--) {
auto [id, node] = *st1.begin();
ka[node] = 1;
ans = node;
st2.insert({ id, node });
st1.erase(st1.begin());
}
cout << ans << endl;
}
else {
int u = k;
for (int i = 19; i >= 0; i--) {
if (ka[up[u][i]]) {
u = up[u][i];
}
}
cout << dp[k] - dp[u] << endl;
ka[u] = 0;
st1.insert({ ind[u], u });
st2.erase({ ind[u], u });
}
}
}
void precalc() {
}
int main() {
// SetIO("teamwork");
FastIO();
int test_case = 1;
// cin >> test_case;
precalc();
int cnt = 1;
while (test_case--) {
solve(cnt++);
}
return 0;
}
