#include <iostream>
#include <vector>
#include <tuple>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <cmath>
#include <array>
#include <random>
#include <string>
#include <cassert>
#include <climits>
#include <algorithm>
#include <unordered_set>
#include <unordered_map>
using namespace std;
#define ll long long
#define f first
#define s second
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template<typename A> void __print(const A &x);
template<typename A, typename B> void __print(const pair<A, B> &p);
template<typename... A> void __print(const tuple<A...> &t);
template<typename T> void __print(stack<T> s);
template<typename T> void __print(queue<T> q);
template<typename T, typename... U> void __print(priority_queue<T, U...> q);
template<typename A> void __print(const A &x) {
bool first = true;
cerr << '{';
for (const auto &i : x) {
cerr << (first ? "" : ","), __print(i);
first = false;
}
cerr << '}';
}
template<typename A, typename B> void __print(const pair<A, B> &p) {
cerr << '(';
__print(p.f);
cerr << ',';
__print(p.s);
cerr << ')';
}
template<typename... A> void __print(const tuple<A...> &t) {
bool first = true;
cerr << '(';
apply([&first] (const auto &...args) { ((cerr << (first ? "" : ","), __print(args), first = false), ...); }, t);
cerr << ')';
}
template<typename T> void __print(stack<T> s) {
vector<T> debugVector;
while (!s.empty()) {
T t = s.top();
debugVector.push_back(t);
s.pop();
}
reverse(debugVector.begin(), debugVector.end());
__print(debugVector);
}
template<typename T> void __print(queue<T> q) {
vector<T> debugVector;
while (!q.empty()) {
T t = q.front();
debugVector.push_back(t);
q.pop();
}
__print(debugVector);
}
template<typename T, typename... U> void __print(priority_queue<T, U...> q) {
vector<T> debugVector;
while (!q.empty()) {
T t = q.top();
debugVector.push_back(t);
q.pop();
}
__print(debugVector);
}
void _print() { cerr << "]\n"; }
template <typename Head, typename... Tail> void _print(const Head &H, const Tail &...T) {
__print(H);
if (sizeof...(T)) cerr << ", ";
_print(T...);
}
#ifdef DEBUG
#define D(...) cerr << "Line: " << __LINE__ << " [" << #__VA_ARGS__ << "] = ["; _print(__VA_ARGS__)
#else
#define D(...)
#endif
int n, q, rt, mn[100005], out[100005], idx, par[100005][20], k, v, ans, depth[100005], tmp;
bool filled[100005];
vector<int> adj[100005];
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
void dfs1(int curr) {
mn[curr] = curr;
for (int i : adj[curr]) {
depth[i] = depth[curr] + 1;
dfs1(i);
mn[curr] = min(mn[curr], mn[i]);
}
}
void dfs2(int curr) {
vector<pair<int, int>> ord;
for (int i : adj[curr]) {
ord.push_back({mn[i], i});
}
sort(ord.begin(), ord.end());
for (auto [m, x] : ord) {
dfs2(x);
}
out[curr] = idx++;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cin >> n >> q;
for (int i = 1; i <= n; i++) {
cin >> par[i][0];
if (!par[i][0]) {
rt = i;
continue;
}
adj[par[i][0]].push_back(i);
}
dfs1(rt);
dfs2(rt);
for (int i = 1; i <= n; i++) {
// cout << i << ": " << out[i] << " " << depth[i] << "\n";
pq.push({out[i], i});
}
for (int i = 1; i < 20; i++) {
for (int j = 1; j <= n; j++) {
par[j][i] = par[par[j][i - 1]][i - 1];
}
}
while (q--) {
cin >> k >> v;
if (k == 1) {
while (v--) {
ans = pq.top().s;
filled[ans] = true;
pq.pop();
}
cout << ans << "\n";
} else {
tmp = v;
for (int i = 19; i >= 0; i--) {
if (filled[par[tmp][i]]) {
tmp = par[tmp][i];
}
}
cout << depth[v] - depth[tmp] << "\n";
filled[tmp] = false;
pq.push({mn[tmp], tmp});
}
}
}
