#include <bits/stdc++.h>
#define ll long long
#define rep(i, n, m) for (ll i = n; i <= m; i ++)
#define rrep(i, n, m) for (ll i = n; i >= m; i --)
using namespace std;
const long long N = 2e5 + 5;
int n, q, a[N], full[N], mi[N], up[20][N];
vector <int> d[N];
void dfs(int u) {
mi[u] = u;
for (int v: d[u])
dfs(v), mi[u] = min(mi[u], mi[v]);
}
int DFS(int u, int &k) {
int lst = 0;
for (int v: d[u]) if (!full[v] && k)
lst = DFS(v, k);
if (k) {
full[u] = true;
k --;
return u;
}
return lst;
}
void del(int u) {
int cnt = 0;
rrep(i, 19, 0) if (full[up[i][u]])
u = up[i][u], cnt += 1 << i;
full[u] = false;
cout << cnt << '\n';
}
void add(int k) {
cout << DFS(0, k) << '\n';
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
//freopen("A.ans", "w", stdout);
cin >> n >> q;
rep(i, 1, n) {
int p; cin >> p;
d[p].push_back(i);
up[0][i] = p;
}
dfs(0);
rep(i, 1, 19) rep(j, 1, n)
up[i][j] = up[i - 1][up[i - 1][j]];
auto cmp = [&] (int u, int v) { return mi[u] < mi[v]; };
rep(i, 1, n) sort(d[i].begin(), d[i].end(), cmp);
int t, x;
while (q --) {
cin >> t >> x;
if (t == 1) add(x);
if (t == 2) del(x);
}
return 0;
}
