#include <bits/stdc++.h>
using namespace std;
const int mxN = 1e5 + 1, LOG = 20;
int N, Q;
int priority[mxN], mnSub[mxN], parentBL[mxN][LOG];
bool hasBall[mxN];
vector<int> adj[mxN];
priority_queue<pair<int, int>> emp;
void dfs1(int node) {
mnSub[node] = 1e9;
for (auto it : adj[node]) {
dfs1(it);
mnSub[node] = min(mnSub[node], mnSub[it]);
}
if (!adj[node].size()) mnSub[node] = node;
}
int idpr = 0;
void dfs2(int node) {
for (auto it : adj[node]) {
dfs2(it);
}
priority[node] = idpr++;
}
void init() {
dfs1(1);
for (int i = 1; i <= N; ++i) {
sort(adj[i].begin(), adj[i].end(), [](int node1, int node2){
return mnSub[node1] < mnSub[node2];
});
}
dfs2(1);
for (int i = 1; i <= N; ++i) emp.push({N - priority[i], i});
for (int i = 1; i < LOG; ++i)
for (int j = 1; j <= N; ++j)
parentBL[j][i] = parentBL[parentBL[j][i-1]][i-1];
}
int inser(int x) {
for (int i = 0; i < x; ++i) {
int curr = emp.top().second;
hasBall[curr] = 1;
emp.pop();
if (i + 1 == x) return curr;
}
return 0;
}
int rem(int x) {
int u = x, k = 0;
for (int i = LOG - 1; i >= 0; --i) {
if (hasBall[parentBL[u][i]]) {
k |= (1 << i);
u = parentBL[u][i];
}
}
hasBall[u] = 0;
emp.push({N - priority[u], u});
return k;
}
void solve() {
cin >> N >> Q;
for (int i = 1; i <= N; ++i) {
cin >> parentBL[i][0];
adj[parentBL[i][0]].push_back(i);
}
init();
while(Q--) {
int k, x;
cin >> k >> x;
if (k == 1) {
cout << inser(x);
}
else {
cout << rem(x);
}
if (Q) cout << '\n';
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
solve();
return 0;
}
