#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define per(i, a, b) for (int i = b - 1; i >= (a); --i)
#define trav(a, x) for (auto &a : x)
#define all(x) x.begin(), x.end()
#define sz(x) x.size()
#define pb push_back
#define umap unordered_map
#define uset unordered_set
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<vi> vvi;
typedef long long ll;
const int INF = 1'000'000'007;
vii graph[100001];
int pos[100001], cur = 0;
map<int, int> empty_nodes;
int find_lo(int u) {
int lo = u;
trav(edge, graph[u]) {
int w, v;
tie(w, v) = edge;
w = find_lo(v);
edge.first = w;
lo = min(lo, w);
}
sort(all(graph[u]));
return lo;
}
void add(int u) {
trav(edge, graph[u]) add(edge.second);
empty_nodes.emplace(cur, u);
pos[u] = cur++;
}
int main() {
cin.tie(0)->sync_with_stdio(0);
cin.exceptions(cin.failbit);
int n, q, root, p[100001], jmp[17][100001];
cin >> n >> q;
rep(i, 1, n + 1) {
cin >> p[i];
if (!p[i])
root = i;
graph[p[i]].emplace_back(0, i);
}
find_lo(root);
add(0);
rep(j, 1, n + 1) jmp[0][j] = p[j];
rep(i, 1, 17) rep(j, 1, n + 1) jmp[i][j] = jmp[i - 1][jmp[i - 1][j]];
rep(i, 0, q) {
int query, val;
cin >> query >> val;
if (query == 1) {
int ans;
rep(j, 0, val) {
ans = empty_nodes.begin()->second;
empty_nodes.erase(empty_nodes.begin());
}
cout << ans << endl;
} else {
int u = val, ans = 0;
per(j, 0, 17) if (!empty_nodes.count(pos[jmp[j][u]])) {
u = jmp[j][u];
ans |= 1 << j;
}
cout << ans << endl;
empty_nodes.emplace(pos[u],u);
}
}
return 0;
}
