#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define N 4000005
#define ff first
#define ss second
#define pb push_back
#define sz(s) (int)s.size()
#define rep(c, a, b) for(c = a; c <= b; c++)
int n, t, q, m = 1, vis[N], par[N], r, dis[N], sp[N][30], vip[N], k[N];
vector <int> v[N];
set <int> ans, jog;
void solve(int x) {
vector <pair<int,int>> s;
for(auto i : v[x]) s.pb({dis[i],i});
sort(s.begin(),s.end());
for(auto i : s) solve(i.ss);
vis[m] = x;
k[x] = m;
ans.insert(m);
m++;
}
void dfs(int x) {
for(auto i : v[x]) {
dfs(i);
dis[x] = min(dis[x],dis[i]);
}
dis[x] = min(x,dis[x]);
}
int main () {
ios::sync_with_stdio(0);cin.tie(0);
cin >> n >> q;
for(int i = 0; i <= n; i++) {
dis[i] = INT_MAX;
}
for(int i = 1; i <= n; i++) {
int x;
cin >> x;
par[i] = x;
sp[i][0] = x;
if(x) v[x].pb(i);
else r = i;
}
for(int i = 1; i <= 20; i++) {
for(int j = 1; j <= n; j++) {
if(sp[j][i - 1]) sp[j][i] = sp[sp[j][i - 1]][i - 1];
}
}
dfs(r);
solve(r);
for(int i = 1; i <= q; i++) {
int x;
cin >> t >> x;
if(t == 1) {
for(int j = 1; j <= x; j++) {
jog.insert(*ans.begin());
ans.erase(*ans.begin());
}
cout << vis[*(--jog.end())] << '\n';
continue;
}
int jg = x, cnt = 0;
for(int j = 20; j >= 0; j--) {
if(jog.find(k[sp[jg][j]]) != jog.end()) {
jg = sp[jg][j];
cnt += (1 << j);
}
}
cout << cnt << '\n';
ans.insert(k[jg]);
jog.erase(k[jg]);
}
}
