#include<bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3","unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
// PBDS Template
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//template <class T>
//using ordered_set = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
//using ordered_multiset = tree<T, null_type, less_equal<T>, rb_tree_tag,tree_order_statistics_node_update>;
// Preset
const int maxn = 200000;
const int INF = 1e9;
const long long int LINF = 1e18;
const long long int mod = 1e9 + 7;
const long long int mod2 = 998244353;
const double e = 2.71828;
const double PI = acos(-1);
const double eps = 1e-10;
#define pb push_back
#define ll long long
//#define int long long
#define ull unsigned long long
#define ld double
#define all(x) x.begin(), x.end()
typedef pair<char,char> pc;
typedef pair<double,double> pdb;
typedef pair<int,int> pi;
typedef pair<ll,ll> pll;
typedef pair<pi,int> pii;
typedef pair<int,ll> pil;
typedef pair<ll,int> pli;
typedef pair<string,int> psi;
typedef pair<int,string> pis;
typedef pair<char,int> pci;
typedef pair<int,char> pic;
typedef pair<int,double> pid;
typedef pair<double,int> pdi;
int dr[4] = {0,1,0,-1}, dc[4] = {1,0,-1,0};
vector<vector<int>> up;
vector<int> adj[maxn+5];
int timer[maxn+5],n,q,root,cnt;
void dfs (int u, int p) {
up[u][0] = p;
for (int i=1; i<17; i++) {
up[u][i] = up[up[u][i-1]][i-1];
}
for (auto v : adj[u]) {
if (v == p) continue;
dfs(v,u);
}
timer[u] = ++cnt;
}
void solve (int &tc) {
cin >> n >> q;
up.assign(n+1, vector<int>(17,0));
for (int i=1; i<=n; i++) {
int p;
cin >> p;
if (p == 0) root = i;
else {
adj[i].pb(p);
adj[p].pb(i);
}
}
dfs(root,0);
set<pi> vis[2];
vector<int> node(n+1,0);
for (int i=1; i<=n; i++) vis[0].insert({timer[i],i});
for (int t=0; t<q; t++) {
int type,ans;
cin >> type;
if (type == 1) {
int k;
cin >> k;
for (int i=0; i<k; i++) {
auto it = vis[0].begin();
if (i == k-1) {
ans = (*it).second;
}
node[(*it).second] = 1;
vis[1].insert(*it);
vis[0].erase(it);
}
cout << ans << '\n';
}
else {
ans = 0;
int x;
cin >> x;
int l = 0, r = n, anc = 0;
while (l<=r) {
int mid = (l+r)/2;
int cur = x;
for (int i=0; i<17; i++) {
if (mid & (1<<i)) cur = up[cur][i];
}
if (cur != 0 && node[cur] == 1) {
// cout << "mid = " << mid << ", cur = " << cur << '\n';
ans = max(ans, mid);
anc = cur;
l = mid+1;
}
else r = mid-1;
}
// cout << t << ' ' << anc << '\n';
auto it = vis[1].find({timer[anc],anc});
node[anc] = 0;
vis[0].insert(*it);
vis[1].erase(it);
cout << ans << '\n';
}
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
// precompute();
// FFT::init_fft();
int tc = 1;
// cin >> tc;
// getchar();
int idx = 1;
while (tc--) {
solve(idx);
idx++;
}
return 0;
}
