#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
struct fenwick {
int n;
vector<int> tree;
fenwick(int _n) : n(_n+10), tree(n+50) {}
void update(int p, int v) {
for(p++; p<n; p+=p&-p) tree[p] += v;
}
int query(int p) {
int ans = 0;
for(p++; p; p-=p&-p) ans += tree[p];
return ans;
}
};
int n, q, up[maxn][20], root, timer=1, in[maxn], id[maxn], out[maxn], mn[maxn];
vector<int> G[maxn], ord;
void dfs(int u) {
in[u] = timer++;
for(int i=1; i<20; i++) up[u][i] = up[up[u][i-1]][i-1];
mn[u] = u;
for(int v : G[u]) {
up[v][0] = u;
dfs(v);
mn[u] = min(mn[u], mn[v]);
}
out[u] = timer++;
}
void dfs2(int u) {
vector<pair<int, int> > ch;
for(int v : G[u]) ch.push_back({ mn[v], v });
sort(ch.begin(), ch.end());
for(auto [_, v] : ch) dfs2(v);
ord.push_back(u);
id[u] = ord.size() - 1;
}
signed main() {
cin >> n >> q;
for(int i=1; i<=n; i++) {
int p; cin >> p;
if(!p) root = i;
else G[p].push_back(i);
}
dfs(root);
dfs2(root);
set<int> st;
for(int i=0; i<n; i++) st.insert(i);
fenwick fwt(2*n);
while(q--) {
int t, u; cin >> t >> u;
if(t == 1) {
int last = 0;
for(int i=0; i<u; i++) {
int p = *st.begin();
st.erase(p);
last = ord[p];
fwt.update(in[ord[p]], 1);
fwt.update(out[ord[p]], -1);
}
cout << last << '\n';
} else {
cout << fwt.query(in[u]) - 1 << '\n';
for(int i=19; i>=0; i--) {
if(!up[u][i]) continue;
if(fwt.query(in[up[u][i]])) u = up[u][i];
}
st.insert(id[u]);
fwt.update(in[u], -1);
fwt.update(out[u], 1);
}
}
}
