#include <bits/stdc++.h>
using namespace std;
#define int long long
#define endl '\n'
const int MOD = 1e9 + 7;
const int INF = LLONG_MAX >> 1;
const int LOG = 25;
signed main() {
ios::sync_with_stdio(false); cin.tie(NULL);
int n, q; cin >> n >> q;
vector<int> tree[n+1];
int par[n+1][LOG], cd[n+1]{};
for (int i = 1; i <= n; i++) {
int c; cin >> c; cd[c]++;
tree[c].push_back(i);
tree[i].push_back(c);
}
set<int> lf;
for (int i = 1; i <= n; i++)
if (cd[i] == 0)
lf.insert(i);
function<void(int, int)> dfs = [&](int u, int p) {
par[u][0] = p;
for (int i = 1; i < LOG; i++)
par[u][i] = par[par[u][i-1]][i-1];
for (auto v : tree[u])
if (v != p)
dfs(v, u);
}; dfs(0, 0);
bool marked[n+1]{};
// Queries
while (q--) {
int t, k; cin >> t >> k;
if (t == 1) {
int ans = 0;
while (k--) {
marked[ans = *lf.begin()] = true;
lf.erase(lf.begin());
if (--cd[par[ans][0]] == 0)
lf.insert(par[ans][0]);
}
cout << ans << endl;
} else {
int r = 0;
for (int j = LOG-1; j >= 0; j--)
if (marked[par[k][j]])
k = par[k][j], r += (1 << j);
cout << r << endl;
marked[k] = false; cd[par[k][0]]++;
lf.insert(k); lf.erase(par[k][0]);
}
}
}
