#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
typedef pair<int, int> ii;
int n, q;
int cnt;
int root;
int p[20][N];
int f[N];
int a[N];
bool in[N];
vector<int> G[N];
void dfs1(int u) {
f[u] = u;
for (auto v : G[u]) {
dfs1(v), f[u] = min(f[u], f[v]);
}
sort(G[u].begin(), G[u].end(), [&] (int x, int y) {
return f[x] < f[y];
});
}
void dfs2(int u) {
for (auto v : G[u]) dfs2(v);
a[u] = cnt--;
}
int main() {
ios::sync_with_stdio(false);
cin >> n >> q;
for (int i = 1; i <= n; ++i) {
cin >> p[0][i];
if (!p[0][i]) root = i;
else {
G[p[0][i]].push_back(i);
}
}
for (int i = 1; i <= 17; ++i) {
for (int j = 1; j <= n; ++j) {
p[i][j] = p[i - 1][p[i - 1][j]];
}
}
cnt = n;
dfs1(root), dfs2(root);
priority_queue<ii> pq;
for (int i = 1; i <= n; ++i) pq.push({a[i], i});
while (q--) {
int t, x; cin >> t >> x;
if (t == 2) {
int res = 0;
for (int i = 17; i >= 0; --i) {
if (in[p[i][x]]) res += (1 << i), x = p[i][x];
}
cout << res << '\n';
in[x] = 0, pq.push({a[x], x});
}
else {
int res = 0;
while (x--) {
int tmp = pq.top().second; pq.pop();
res = tmp, in[tmp] = 1;
}
cout << res << '\n';
}
}
}
