#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ar array
const int N = 1e5+5,LGN = 18;
int n,r,q,p[N],mn[N],ord[N],have[N],lift[N][LGN];
set<ar<int,2>> order;
vector<int>adj[N];
void dfs(int u,int p) {
if(adj[u].empty()) mn[u] = u;
for (int v : adj[u]) {
if (v == p) continue;
dfs(v,u);
mn[u] = min(mn[u],mn[v]);
}
}
void dfs2(int u,int p) {
for (int v : adj[u]) {
if (v == p) continue;
dfs2(v,u);
}
ord[u] = (int)order.size() + 1;
order.insert({ord[u],u});
}
void build(){
for (int i = 0; i <= n;i++) {
lift[i][0] = p[i];
}
for (int lg = 1; lg < LGN;lg++) {
for (int i = 0; i <= n;i++) {
lift[i][lg] = lift[lift[i][lg - 1]][lg - 1];
}
}
}
int get_kth(int u, int k) {
int ans = u;
for (int i = LGN - 1; i >= 0;i--) {
if (k & (1 << i)) {
ans = lift[ans][i];
}
}
return ans;
}
bool check(int u,int x) {
return have[get_kth(u,x)];
}
void solve() {
cin >> n >> q;
for (int i = 0; i < n;i++) mn[i] = i, have[i] = 0;
for (int i = 0; i < n;i++) {
cin >> p[i],--p[i];
if (p[i] == -1) {
r = i;
p[i] = n;
p[n] = n;
have[n] = 0;
continue;
}
adj[p[i]].push_back(i);
}
dfs(r,r);
for (int i = 0; i < n;i++) {
sort(adj[i].begin(),adj[i].end(),[&](int x,int y) {
return mn[x] < mn[y];
});
}
dfs2(r,r);
build();
while(q--) {
int qt,k;
cin >> qt >> k;
if (qt == 1) {
for (int i= 0; i < k - 1;i++) {
have[(*order.begin())[1]] = 1;
order.erase(order.begin());
}
have[(*order.begin())[1]] = 1;
cout << (*order.begin())[1] + 1 << "\n";
order.erase(order.begin());
}else {
--k;
int L = 0, R = n, ans = 0;
while (L <= R) {
int M = (L + R) / 2;
if (check(k,M)) L = M + 1,ans = M;
else R = M - 1;
}
int pr = get_kth(k,ans);
order.insert({ord[pr],pr});
have[pr] = 0;
cout << ans << "\n";
}
}
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int t = 1;
// cin >> t;
while (t--) {
solve();
cout << "\n";
}
return 0;
}
