#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define pb push_back
#define ld long double
#define fi first
#define se second
#define ll long long
#define ss(x) (int) x.size()
#define mp make_pair
#define FOR(i, n) for(int i = 1; n >= i; ++i)
using namespace std;
using namespace __gnu_pbds;
const int nax = 1e5 + 5, pod = (1 << 19), mod = 998244353;
const ll inf = 1e18;
int n, q;
int root;
vector <int> v[nax];
int black[nax], lca[nax][17];
int dp[nax];
int pr[nax];
int fre = 0;
void dfs(int node) {
dp[node] = node;
for(auto it: v[node]) {
dfs(it);
dp[node] = min(dp[node], dp[it]);
lca[it][0] = node;
}
}
void go(int node) {
vector <pair<int, int>> e;
for(auto it: v[node]) {
e.pb(mp(dp[it], it));
}
sort(e.begin(), e.end());
for(auto it: e) {
go(it.se);
}
pr[node] = fre++;
}
set <pair<int, int>> s;
int add() {
pair<int, int> x = *s.begin();
black[x.se] = 1;
s.erase(s.begin());
return x.se;
}
int main() {
cin.tie(0);
ios_base::sync_with_stdio(0);
cin >> n >> q;
for(int i = 1; i <= n; ++i) {
int p;
cin >> p;
if(!p)
root = i;
else
v[p].pb(i);
}
dfs(root);
for(int j = 1; j <= 16; ++j)
for(int i = 1; i <= n; ++i)
lca[i][j] = lca[lca[i][j - 1]][j - 1];
go(root);
for(int i = 1; i <= n; ++i)
s.insert(mp(pr[i], i));
while(q--) {
int type;
int k;
cin >> type >> k;
if(type == 1) {
int res = -1;
while(k--) {
res = add();
}
cout << res << endl;
}
else {
int w = k;
int dis = 0;
for(int i = 16; 0 <= i; --i) {
int r = lca[w][i];
if(!r)
continue;
if(black[r]) {
w = r;
dis += (1 << i);
}
}
black[w] = 0;
s.insert(mp(pr[w], w));
cout << dis << endl;
}
}
return 0;
}
