#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
#define all(x) (x).begin(),(x).end()
#define X first
#define Y second
#define sep ' '
#define endl '\n'
#define debug(x) cerr << #x << ": " << x << endl;
const ll MAXN = 1e6 + 10;
const ll LOG = 20;
int n, rt, par[MAXN][LOG], q, tin[MAXN], mn[MAXN], f[MAXN], t;
vector<int> adj[MAXN];
priority_queue<int> pq;
bool used[MAXN];
void dfs1(int v) {
mn[v] = v;
for (int u : adj[v]) {
dfs1(u);
mn[v] = min(mn[v], mn[u]);
}
}
void dfs2(int v) {
tin[v] = ++t;
f[t] = v;
sort(all(adj[v]), [] (int i, int j) {
return mn[i] > mn[j];
});
for (int u : adj[v])
dfs2(u);
}
inline int add() {
int v = f[pq.top()];
pq.pop();
used[v] = true;
return v;
}
inline int remove(int v) {
int ans = 0;
for (int i = LOG - 1; i >= 0; i--) {
if (used[par[v][i]]) {
ans ^= (1 << i);
v = par[v][i];
}
}
used[v] = false;
pq.push(tin[v]);
return ans;
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
cin >> n >> q;
for (int i = 1; i <= n; i++) {
cin >> par[i][0];
rt = (par[i][0] ? rt : i);
pq.push(i);
adj[par[i][0]].push_back(i);
}
for (int i = 1; i < LOG; i++)
for (int v = 1; v <= n; v++)
par[v][i] = par[par[v][i - 1]][i - 1];
dfs1(rt);
dfs2(rt);
while (q--) {
int c, x;
cin >> c >> x;
if (c == 1) {
int ans = 0;
while (x--) ans = add();
cout << ans << endl;
} else {
cout << remove(x) << endl;
}
}
return 0;
}
