#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif
const int N = 1e5 + 5, LG = 17;
int n, q;
int a[N], b[N], pr[LG][N];
bool alive[N];
vector<int> g[N];
int ind;
void dfs(int u, bool keep) {
if (keep) {
sort(g[u].begin(), g[u].end(), [&](int i, int j) {
return a[i] < a[j];
});
for (int v : g[u]) {
dfs(v, 1);
}
b[u] = ++ind;
return;
}
a[u] = u;
for (int v : g[u]) {
dfs(v, 0);
a[u] = min(a[u], a[v]);
}
}
int main() {
ios::sync_with_stdio(false); cin.tie(nullptr);
cin >> n >> q;
for (int i = 1; i <= n; ++i) {
cin >> pr[0][i];
g[pr[0][i]].push_back(i);
}
for (int j = 1; j < LG; ++j) {
for (int i = 1; i <= n; ++i) {
pr[j][i] = pr[j - 1][pr[j - 1][i]];
}
}
dfs(0, 0);
dfs(0, 1);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
for (int i = 1; i <= n; ++i) {
pq.push({b[i], i});
}
while (q--) {
int t; cin >> t;
if (t == 1) {
int k; cin >> k;
int lst = 0;
while (k--) {
auto [x, u] = pq.top(); pq.pop();
lst = u;
alive[u] = 1;
}
cout << lst << "\n";
} else {
int u; cin >> u;
int res = 0;
for (int j = LG - 1; ~j; --j) {
if (alive[pr[j][u]]) {
u = pr[j][u];
res += 1 << j;
}
}
alive[u] = 0;
pq.push({b[u], u});
cout << res << "\n";
}
}
return 0;
}
