#include "bits/stdc++.h"
using namespace std;
const int N = (int) 1e5 + 22;
vector<int> g[N];
int n, q, dp[N], rt, uk = 0, ord[N], up[N][20];
void dfs(int v) {
dp[v] = v;
for (int j = 1; j < 20; j++) {
if (up[v][j - 1] == -1) {
up[v][j] = -1;
continue;
}
up[v][j] = up[up[v][j - 1]][j - 1];
}
for (auto u : g[v]) {
up[u][0] = v;
dfs(u);
dp[v] = min(dp[v], dp[u]);
}
std::sort(g[v].begin(), g[v].end(), [&] (int x, int y) { return dp[x] < dp[y]; });
}
void dfs2(int v) {
for (auto u : g[v]) {
dfs2(u);
}
ord[v] = uk++;
}
void solve() {
cin >> n >> q;
for (int i = 0; i < n; i++) {
int p;
cin >> p;
p--;
if (p == -1) {
rt = i;
} else {
g[p].push_back(i);
}
}
up[rt][0] = -1;
dfs(rt);
dfs2(rt);
set<pair<int, int>> life;
for (int i = 0; i < n; i++) {
life.insert({ord[i], i});
}
while (q--) {
int t, x;
cin >> t >> x;
if (t == 1) {
int ans = 0;
while (x--) {
int v = life.begin()->second;
ans = v;
life.erase(life.begin());
}
cout << ans + 1 << '\n';
} else {
x--;
int v = x, dist = 0;
for (int j = 19; j >= 0; j--) {
int u = up[v][j];
if (u == -1) {
continue;
}
if (life.find({ord[u], u}) == life.end()) {
dist += (1 << j);
v = u;
}
}
life.insert({ord[v], v});
cout << dist << '\n';
}
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t = 1;
// cin >> t;
while (t--) {
solve();
}
}
