# include <bits/stdc++.h>
using namespace std;
#define f first
#define s second
// #define int long long
#define pii pair <int, int>
#define pb push_back
const int N = 3e5 + 5;
int t,n,a[N], par[N][20], mn[N], idx[N],q,rt,del[N];
vector <int> v[N],vec, ord;
set <int> s;
void dfs(int a, int p) {
mn[a] = a;
par[a][0] = p;
for (int i = 1; i <= 18; i++) {
if (par[a][i - 1]) par[a][i] = par[par[a][i - 1]][i - 1];
}
for (int to : v[a]) {
if (to == p) continue;
dfs(to, a);
mn[a] = min(mn[a], mn[to]);
}
}
bool cmp(int a, int b) {
return mn[a] < mn[b];
}
void dfs1(int a, int p) {
vector <int> vec;
for (int to : v[a]) {
if (to == p) continue;
vec.pb(to);
}
sort(vec.begin(),vec.end(), cmp);
for (int to : vec){
dfs1(to, a);
}
s.insert(a);
ord.pb(a);
}
main() {
std::ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0);
cin>>n>>q;
for (int i = 1; i <= n; i++) {
int p;
cin>>p;
if (p == 0) {
rt = i; continue;
}
v[i].pb(p);
v[p].pb(i);
}
ord.pb(0);
dfs(rt, 0);
dfs1(rt, 0);
for (int i = 1; i <= n; i++) {
idx[ord[i]] = i;
}
while (q--) {
int ty;
cin>>ty;
if (ty == 1) {
int k, ans = 0; cin>>k;
while(k--) {
int x = ord[*s.begin()];
del[x] = 1;
ans = x;
s.erase(s.begin());
}
cout<<ans<<"\n";
continue;
}
int cur, ans = 0, x;
cin>>x; cur = x;
for (int i = 18; i >= 0; i--) {
if (par[cur][i] && del[par[cur][i]]) cur = par[cur][i], ans += (1<<i);
}
del[cur] = 0; s.insert(idx[cur]);
cout<<ans<<"\n";
}
}
