#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ull unsigned long long
#define pb(e) push_back(e)
#define sv(a) sort(a.begin(),a.end())
#define sa(a,n) sort(a,a+n)
#define mp(a,b) make_pair(a,b)
#define vf first
#define vs second
#define ar array
#define all(x) x.begin(),x.end()
const int inf = 0x3f3f3f3f;
const int mod = 1000000007;
const double PI=3.14159265358979323846264338327950288419716939937510582097494459230;
bool remender(ll a , ll b){return a%b;}
const int N = 100003, L = 25;
vector<int> adj[N];
int tout[N] , timer , cur[N] , up[N][L] , deg[N] , sweepmo[N];
void drymo(int node){
sweepmo[node] = node;
for(int i : adj[node]){
drymo(i);
sweepmo[node] = min(sweepmo[node] , sweepmo[i]);
}
}
void dfs(int node , int par){
up[node][0] = par;
for(int i = 1; i < L; i++){
up[node][i] = up[up[node][i-1]][i-1];
}
vector<pair<int,int>> v;
for(int i : adj[node]){
deg[i] = deg[node] + 1;
v.pb(mp(sweepmo[i] , i));
}
sv(v);
for(auto i : v){
dfs(i.vs , node);
}
tout[node] = timer++;
}
pair<int,int> find(int node){
int res = deg[node];
for(int i = L - 1; i >= 0; i--){
if(cur[up[node][i]] == 1){
node = up[node][i];
}
}
return mp(res - deg[node] , node);
}
void solve(){
int n;
cin >> n;
int q;
cin >> q;
int root;
for(int i = 1; i < n + 1; i++){
int x;
cin >> x;
if(x == 0)root = i;
else adj[x].pb(i);
}
drymo(root);
timer = 0;
deg[root] = 0;
dfs(root , root);
memset(cur,0,sizeof cur);
set<pair<int,int>> s;
for(int i = 1; i <= n; i++){
s.insert(mp(tout[i] , i));
}
while(q--){
int type;
cin >> type;
int cnt;
cin >> cnt;
if(type == 1){
int ans;
while(cnt > 0){
pair<int,int> p = *s.begin();
s.erase(s.begin());
cur[p.vs] = 1;
ans = p.vs;
cnt--;
}
cout << ans << '\n';
}
else {
pair<int,int> ans = find(cnt);
cout << ans.vf << '\n';
cur[ans.vs] = 0;
s.insert(mp(tout[ans.vs] , ans.vs));
}
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
//int t;cin >> t;while(t--)
solve();
return 0;
}
