#include <bits/stdc++.h>
using namespace std;
const int mxN = 1e5 + 10;
const int mxB = 21;
vector<int> adj[mxN];
int mn[mxN], ball[mxN], dp[mxN][mxB];
vector<int> ord;
void dfs(int u = 1){
mn[u] = u;
for(int j = 1; j < mxB; ++j){
dp[u][j] = dp[dp[u][j - 1]][j - 1];
}
for(auto it : adj[u]){
dp[it][0] = u;
dfs(it);
mn[u] = min(mn[u], mn[it]);
}
}
void dfs2(int u = 1){
vector<pair<int, int>> val;
for(auto it : adj[u]){
val.push_back({mn[it], it});
}
sort(val.begin(), val.end());
for(auto it : val){
dfs2(it.second);
}
ord.push_back(u);
}
int up_most(int u){
for(int i = mxB - 1; i >= 0; --i){
if(ball[dp[u][i]]){
u = dp[u][i];
}
}
return u;
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(nullptr); cout.tie(nullptr);
int n, q;
cin >> n >> q;
int root = 1;
for(int i = 1, par; i <= n; ++i){
cin >> par;
adj[par].push_back(i);
if(par == 0) root = i;
}
dfs(root);
dfs2(root);
set<pair<int, int>> empty;
vector<int> pos(n + 5, 0);
for(int i = 0; i < (int) ord.size(); ++i){
empty.insert({i, ord[i]});
pos[ord[i]] = i;
}
auto remove = [&](int x) -> void {
int top = up_most(x);
if(top == x){
empty.insert({pos[x], x});
}else{
}
};
while(q--){
int t, k;
cin >> t >> k;
if(t == 1){
int last = 0;
while(k--){
auto tp = *empty.begin();
empty.erase(tp);
last = tp.second;
ball[tp.second] = 1;
}
cout << last << "\n";
}else{
remove(k);
}
}
return 0;
}
