#include "bits/stdc++.h"
using namespace std;
void abc() {cout << endl;}
template <typename T, typename ...U> void abc(T a, U ...b) {
cout << a << ' ', abc(b...);
}
template <typename T> void printv(T l, T r) {
while (l != r) cout << *l << " \n"[++l == r];
}
template <typename A, typename B> istream& operator >> (istream& o, pair<A, B> &a) {
return o >> a.first >> a.second;
}
template <typename A, typename B> ostream& operator << (ostream& o, pair<A, B> a) {
return o << '(' << a.first << ", " << a.second << ')';
}
template <typename T> ostream& operator << (ostream& o, vector<T> a) {
bool is = false;
for (T i : a) {o << (is ? ' ' : '{'), is = true, o << i;}
return o << '}';
}
#ifdef local
#define test(args...) abc("[" + string(#args) + "]", args)
#else
#define test(args...) void(0)
#endif
using ll = long long;
vector<int> adj[100005];
int jmp[100005][20];
int depth[100005];
vector<int> trav;
bool seen[100005];
map<int, int> fromp, fromv;
int mn[100005];
void dfs(int node, int par = -1) {
if (!seen[node]) {
seen[node] = true;
trav.push_back(node);
}
for (int i = 1; i < 20; i++) {
jmp[node][i] = jmp[jmp[node][i-1]][i-1];
}
for (auto nxt : adj[node]) {
depth[nxt] = depth[node] + 1;
jmp[nxt][0] = node;
dfs(nxt, node);
}
}
void dfs2(int node) {
mn[node] = node;
for (auto nxt : adj[node]) {
dfs2(nxt);
mn[node] = min(mn[node], mn[nxt]);
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
// freopen("test.txt", "r", stdin);
// freopen("", "w", stdout);
int n, q; cin >> n >> q;
int root = 0;
for (int i = 1; i <= n; i++) {
int t; cin >> t;
if (t == 0) {
root = i;
continue;
}
adj[t].push_back(i);
}
dfs2(root);
for (int i = 1; i <= n; i++) {
sort(adj[i].begin(), adj[i].end(), [](int a, int b) {
return mn[a] > mn[b];
});
}
jmp[root][0] = 1;
depth[root] = 1;
dfs(root);
reverse(trav.begin(), trav.end());
// for (auto a : trav) cout << a << " ";
set<int> st;
for (int i = 1; i <= n; i++) {
fromp[i] = trav[i - 1];
fromv[trav[i-1]] = i;
st.insert(i);
}
// for (auto x: trav) cout << x << " ";
// cout << endl;
// cout << fromp[184] << " " << fromp[185] << " " << fromp[183] << endl;
// cout << fromv[212] << endl;
for (int i = 0; i < q; i++) {
int a, b; cin >> a >> b;
if (a == 1) {
// add
int lst = -1;
while (b) {
auto addedto = *st.begin();
st.erase(addedto);
lst = fromp[addedto];
b--;
}
cout << lst << "\n";
} else {
// remove node b
int tempb = b;
int dist = 0;
for (int i = 19; i >= 0; i--) {
int jmpto = jmp[tempb][i];
if (st.count(fromv[jmpto]) || depth[tempb] - (1 << i) < 1) {
continue;
}
dist += (1 << i);
tempb = jmp[tempb][i];
}
int idx = fromv[tempb];
st.insert(idx);
cout << dist << "\n";
}
}
}
