#include<iostream>
#include<stack>
#include<map>
#include<vector>
#include<string>
#include<unordered_map>
#include <queue>
#include<cstring>
#include<limits.h>
#include<cmath>
#include<set>
#include<algorithm>
#include<bitset>
#include<list>
using namespace std;
#define ll long long
#define f first
#define endl "\n"
#define s second
#define pii pair<int,int>
#define ppii pair<int,pii>
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define F(n) for(int i=0;i<n;i++)
#define lb lower_bound
#define ub upper_bound
//#define p push
#define pb push_back
#define fastio ios::sync_with_stdio(false);cin.tie(NULL);
using namespace std;
#define int long long
const int mxn=1e5,mod=69,lg=30,root=80,inf=1e18;
vector<ppii>adj[mxn+10];
int up[mxn+10][lg+5],h[mxn+10],st,go[mxn+10];
bitset<mxn+10>on;
int ch=0;
int dfs(int cur,int p){
int cm=inf;
for(auto &i:adj[cur]){
h[i.f]=h[cur]+1;
ch=max(ch,h[i.f]);
int k=dfs(i.f,cur);
cm=min(cm,k);
i.s.f=k;
}
return min(cm,cur);
}
int solve(int cur,int p){
int cm=inf;
for(auto &i:adj[cur])cm=min(cm,i.s.f);
for(auto &i:adj[cur]){
i.s.s=solve(i.f,cur);
if(i.s.f==cm)go[cur]=i.s.s;
}
if(cm==inf)return go[cur]=cur;
return go[cur];
}
int32_t main(){
fastio
int n,m;cin>>n>>m;
for(int i=1;i<=n;i++){
int a;cin>>a;
if(a==0){
st=i;
continue;
}
adj[a].pb({i,{-1,-1}});
up[i][0]=a;
}
priority_queue<pii>pq;
dfs(st,-1);
solve(st,-1);
for(int j=1;j<=lg;j++)for(int i=1;i<=n;i++)up[i][j]=up[up[i][j-1]][j-1];
while(m--){
int t;cin>>t;
if(t==1){
int k;cin>>k;
int ans=0;
for(int j=0;j<k;j++){
while(!pq.empty()&&!on[pq.top().s])pq.pop();
while(!pq.empty()&&on[up[pq.top().s][0]])pq.pop();
if(pq.empty())pq.push({h[go[st]],go[st]}),on[go[st]]=true,ans=go[st];
else{
int cur=pq.top().s;
cur=up[cur][0];
int cm=inf;
pq.pop();
for(auto i:adj[cur])if(!on[i.f])cm=min(cm,i.s.f);
for(auto i:adj[cur]){
if(i.s.f==cm){
pq.push({h[i.s.s],i.s.s}),on[i.s.s]=true,ans=i.s.s;
break;
}
}
if(cm==inf){
on[cur]=true;
ans=cur;
pq.push({h[cur],cur});
}
}
}
cout<<ans<<'\n';
}
else{
int x,y,diff;cin>>x;
y=x;
for(int i=lg;i>=0;i--)if(on[up[x][i]])x=up[x][i];
diff=h[y]-(h[x]+1);
for(int i=0;i<=lg;i++)if(diff&(1<<i))y=up[y][i];
on[x]=false;
if(diff!=-1)pq.push({h[y],y});
else{for(auto i:adj[x])pq.push({h[i.f],i.f});}
cout<<diff+1<<'\n';
}
}
}
