#include <bits/stdc++.h>
#define DEBUG 0
using namespace std;
const int MAX_N = 1e5 + 10;
int timer;
vector <int> graph[MAX_N];
int depth[MAX_N], parent[MAX_N][20];
int minimum[MAX_N];
int st[MAX_N], pos[MAX_N];
bool state[MAX_N];
bool tree[4 * MAX_N];
int get_min(int u) {
minimum[u] = u;
for(auto v : graph[u]) {
depth[v] = depth[u] + 1;
minimum[u] = min(minimum[u], get_min(v));
}
return minimum[u];
}
void postorder(int u) {
for(auto v : graph[u]) {
postorder(v);
}
timer++;
st[u] = timer;
pos[timer] = u;
}
int jump(int u, int k) {
for(int i = 0; i < 20; i++) {
if(k & (1<<i)) {
u = parent[u][i];
}
}
return u;
}
void update(int idx, int l, int r, int q, bool v) {
if(l == r) {
tree[idx] = v;
return;
}
int mid = (l + r) / 2;
if(q <= mid) {
return void(update(idx * 2, l, mid, q, v));
}
update(idx * 2 + 1, mid + 1, r, q, v);
tree[idx] = tree[idx * 2] & tree[idx * 2 + 1];
}
int query(int idx, int l, int r) {
if(l == r) {
return l;
}
int mid = (l + r) / 2;
if(tree[idx * 2] == false) {
return query(idx * 2, l, mid);
}
return query(idx * 2 + 1, mid + 1, r);
}
int main() {
cin.tie(0)->sync_with_stdio(0);
int N, Q;
cin >> N >> Q;
int root = 1;
for(int i = 1; i <= N; i++) {
cin >> parent[i][0];
graph[parent[i][0]].push_back(i);
if(parent[i][0] == 0) {
root = i;
}
}
get_min(root);
for(int i = 1; i <= N; i++) {
sort(graph[i].begin(), graph[i].end(), [&](const int &a, const int &b) {
return minimum[a] < minimum[b];
});
}
postorder(root);
depth[0] = -1;
for(int j = 1; j < 20; j++) {
for(int i = 1; i <= N; i++) {
parent[i][j] = parent[parent[i][j - 1]][j - 1];
}
}
while(Q--) {
int t, idx;
cin >> t;
if(t == 1) {
int k;
cin >> k;
while(k > 0) {
idx = query(1, 1, N);
while(k > 0 and state[pos[idx]] == false) {
state[pos[idx]] = true;
update(1, 1, N, idx, true);
k--;
if(k > 0) {
idx++;
}
}
}
cout << pos[idx] << '\n';
}
else {
int x;
cin >> x;
int l = 0, r = depth[x], res;
while(l <= r) {
int mid = (l + r) / 2;
if(state[jump(x, mid)] == true) {
res = mid;
l = mid + 1;
}
else {
r = mid - 1;
}
}
cout << res << '\n';
idx = jump(x, res);
state[idx] = false;
update(1, 1, N, st[idx], false);
}
}
return 0;
}
