#include<bits/stdc++.h>
using namespace std;
const int N = 1e5 + 5;
int n , q;
vector<int> adj[N];
int S[N] , P[N][20] , R , A[N] , B[N] ,C[N], b;
void dfs(int u, int p){
S[u]=u;
P[u][0]= p;
for(int i = 1; i<= 18; ++i) P[u][i]= P[P[u][i - 1]][i - 1];
for(int v : adj[u]){
dfs(v,u);
S[u] = min(S[u], S[v]);
}
}
void DFS(int u){
for(int v : adj[u]) DFS(v);
B[++b] = u;
}
bool cmp(int a, int b){
return S[a] < S[b];
}
int k = 0;
int Q(int u){
for(int i = 17; ~i; --i){
int y = P[u][i];
if(C[y]) u = y ,k += (1 <<i);
}
return u;
}
int main (){
ios_base::sync_with_stdio(0); cin.tie(0);
cin >> n >> q;
int a;
for(int i= 1; i <=n; ++i){
cin >> a;
if(a==0)R = i;
else adj[a].emplace_back(i);
}
for(int i = 1;i <= n; ++i) S[i] = 2e9;
dfs(R,0);
for(int i= 1; i<= n; ++i)sort(adj[i].begin() ,adj[i].end() , cmp);
DFS(R);
//for(int i = 1; i<= n; ++i)cout << B[i] << " ";cout << endl;
for(int i = 1; i <= n; ++i) A[B[i]] = i;
set<int> s;
for(int i = 1; i<= n; ++i)s.insert(i);
while(q--){
int d;
cin >> d;
if(d==1){
int x;
cin >> x;
int g = 0;
while(x--){
g = *s.begin();
s.erase(s.begin());
C[B[g]] =1;
}
cout << B[g]<<endl;
}else{
int u; cin>>u;
int h = Q(u);
cout << k << endl;k=0;
s.insert(A[h]);
C[h]=0;
}
}
return 0;
}
