#include <bits/stdc++.h>
#define FOR(i, x, y) for (int i = x; i < y; i++)
typedef long long ll;
using namespace std;
struct Node {
int id, order;
};
bool operator<(Node A, Node B) {
return A.order < B.order;
}
vector<int> graph[100001];
int ancestor[100001][20], least_child[100001], order[100001], cnt = 1;
bool emp[100001];
set<Node> no_ball;
bool cmp(int A, int B) {
return least_child[A] < least_child[B];
}
void find_least_children(int node = 0) {
least_child[node] = node;
FOR(i, 1, 20) {
if (!ancestor[node][i - 1]) break;
ancestor[node][i] = ancestor[ancestor[node][i - 1]][i - 1];
}
for (int i : graph[node]) {
ancestor[i][0] = node;
find_least_children(i);
least_child[node] = min(least_child[node], least_child[i]);
}
}
void dfs(int node = 0) {
for (int i : graph[node]) dfs(i);
order[node] = cnt++;
if (node) no_ball.insert({node, order[node]});
emp[node] = true;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n, q;
cin >> n >> q;
FOR(i, 1, n + 1) {
int p;
cin >> p;
graph[p].push_back(i);
}
find_least_children();
FOR(i, 1, n + 1) sort(graph[i].begin(), graph[i].end(), cmp);
dfs();
while (q--) {
int t, x;
cin >> t >> x;
if (t == 1) {
FOR(i, 1, x) {
emp[(*no_ball.begin()).id] = false;
no_ball.erase(no_ball.begin());
}
cout << (*no_ball.begin()).id << '\n';
emp[(*no_ball.begin()).id] = false;
no_ball.erase(no_ball.begin());
} else {
int lca = x, ans = 0;
for (int i = 19; ~i; i--) {
if (ancestor[lca][i] && !emp[ancestor[lca][i]]) {
ans += (1<<i);
lca = ancestor[lca][i];
}
}
emp[lca] = true;
no_ball.insert({lca, order[lca]});
cout << ans << '\n';
}
}
return 0;
}
