#include <iostream>
#include <cmath>
#include <unordered_map>
#include <map>
#include <set>
#include <queue>
#include <vector>
#include <string>
#include <iomanip>
#include <algorithm>
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
using namespace std;
typedef long long ll;
ll linf = 1e15+1;
inline void scoobydoobydoo(){
ios::sync_with_stdio(false);
ios_base::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
}
const int MAXN = 2e5+1;
int parent[MAXN];
int binPar[MAXN][20];
vector<int> children[MAXN];
int childs[MAXN];
int vals[MAXN];
int minInSubtree[MAXN];
int root;
int indexToVal[MAXN];
int valToIndex[MAXN];
int hasBall[MAXN];
int indexToNode[MAXN];
int nodeToIndex[8*MAXN];
int initMinInSubtree(int node = root){
int mini = node;
for (auto& e : children[node]){
mini = min(mini, initMinInSubtree(e));
}
return minInSubtree[node] = mini;
}
int x = 0;
int n, q;
void initVals(int node = root){
set<pair<int, int>> s;
for (auto& e : children[node]){
s.insert({minInSubtree[e], e});
}
for (auto& p : s){
initVals(p.second);
}
indexToVal[x] = node;
valToIndex[node] = x;
vals[x++] = node;
return;
}
void initBinPar(){
for (int i = 1; i <= n; i++){
binPar[i][0] = parent[i];
}
for (int j = 1; j < 20; j++){
for (int i = 1; i <= n; i++){
binPar[i][j] = binPar[binPar[i][j-1]][j-1];
}
}
return;
}
pair<int, int> lastBallParent(int node){
if (!hasBall[parent[node]])return {node, 0};
int rolledBalls = 0;
for (int i = 19; i >= 0; i--){
if (hasBall[binPar[node][i]]){
node = binPar[node][i];
rolledBalls += (1 << i);
}
}
return {node, rolledBalls};
}
int ST[8*MAXN];
int leftOf[8*MAXN], rightOf[8*MAXN];
void buildTree(int l, int r, int node = 1){
leftOf[node] = l;
rightOf[node] = r;
if (l == r){
ST[node] = 0;
indexToNode[l] = node;
nodeToIndex[node] = l;
return;
}
int mid = (l+r)/2;
buildTree(l, mid, 2*node);
buildTree(mid+1, r, 2*node+1);
ST[node] = 0;
}
void update1(int node){
if (node == 0)return;
ST[node] = min(ST[2*node], ST[2*node+1]);
return update1(node/2);
}
void update(int node, int w){
node = indexToNode[node];
ST[node] = w;
update1(node/2);
}
int closestEmpty(int node = 1){
if (leftOf[node] == rightOf[node]){
return nodeToIndex[node];
}
int a = 2*node, b = 2*node+1;
if (ST[a] == 0)return closestEmpty(a);
return closestEmpty(b);
}
int main(){
scoobydoobydoo();
cin >> n >> q;
for (int i = 1; i <= n; i++){
cin >> parent[i];
children[parent[i]].push_back(i);
childs[parent[i]]++;
if (parent[i] == 0){
root = i;
//parent[i] = i;
}
}
initMinInSubtree();
initVals();
initBinPar();
buildTree(0, n-1);
vector<ll> ans;
while (q--){
int t; cin >> t;
if (t == 1){
int k; cin >> k;
int latest = -1;
for (int i = 0; i < k; i++){
int ind = closestEmpty();
latest = ind;
hasBall[indexToVal[ind]] = 1;
update(ind, 1);
}
ans.push_back(indexToVal[latest]);
} else {
int x; cin >> x;
pair<int, int> ballParent = lastBallParent(x);
int indToRemove = valToIndex[ballParent.first];
//cout << "SAVEME " << ballParent.first << " " << ballParent.second << endl;
update(indToRemove, 0);
hasBall[ballParent.first] = 0;
ans.push_back(ballParent.second);
}
}
for (auto& e : ans){
cout << e << endl;
}
return 0;
}
