#include <iostream>
#include <set>
#include <vector>
using namespace std;
set<pair<int, int>> s[100005];
vector<int> g[100005];
int l[100005][18], da[100005], d[100005], f[100005], h;
void dfs(int x) {
d[x] = x;
for (int w : g[x]) {
dfs(w);
d[x] = min(d[x], d[w]);
}
}
void dfs2(int x) {
f[x] = x;
for (int w : g[x]) s[x].insert({d[w], w});
for (auto w : s[x]) {
dfs2(w.second);
if (w.first == (*s[x].begin()).first) f[x] = f[w.second];
}
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
int n, q;
cin >> n >> q;
for (int i = 1; i <= n; i++) {
int x;
cin >> x;
l[i][0] = x;
g[x].push_back(i);
}
dfs(0);
dfs2(0);
h = f[0];
for (int i = 1; i <= 17; i++) {
for (int j = 1; j <= n; j++) {
l[j][i] = l[l[j][i - 1]][i - 1];
}
}
for (int jj = 0; jj < q; jj++) {
int w, x;
cin >> w >> x;
if (w == 1) {
int res = 0;
for (int i = 1; i <= x; i++) {
res = h;
da[h] = 1;
s[l[h][0]].erase({d[h], h});
if (!s[l[h][0]].empty()) {
int k = (*s[l[h][0]].begin()).second;
h = f[k];
}
else h = l[h][0];
}
cout << res << '\n';
}
else {
int res = 0;
for (int i = 17; i >= 0; i--) {
if (da[l[x][i]] == 1) {
x = l[x][i];
res += (1 << i);
}
}
s[l[x][0]].insert({d[x], x});
h = x;
da[h] = 0;
cout << res << '\n';
}
}
}
