#include <bits/stdc++.h>
#define FAST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);cerr.tie(0)
#define mp make_pair
#define xx first
#define yy second
#define pb push_back
#define pf push_front
#define popb pop_back
#define popf pop_front
#define all(x) x.begin(),x.end()
#define ff(i,a,b) for (int i = a; i < b; i++)
#define fff(i,a,b) for (int i = a; i <= b; i++)
#define bff(i,a,b) for (int i = b-1; i >= a; i--)
#define bfff(i,a,b) for (int i = b; i >= a; i--)
using namespace std;
long double typedef ld;
unsigned int typedef ui;
long long int typedef li;
pair<int,int> typedef pii;
pair<li,li> typedef pli;
pair<ld,ld> typedef pld;
vector<vector<int>> typedef graph;
unsigned long long int typedef ull;
//const int mod = 998244353;
const int mod = 1000000007;
//Note to self: Check for overflow
int rootcina=-1;
vector<vector<pii>> g(100005);
int mk[100005]; //minimalni node u subtree-u
int tin[100005];
int kad[100005];
int up[20][100005];
int VREME=0;
void cringedfs(int p, int q)
{
mk[p]=p;
ff(i,0,(int)g[p].size()) if (g[p][i].yy!=q)
{
cringedfs(g[p][i].yy,p);
mk[p]=min(mk[p],mk[g[p][i].yy]);
g[p][i].xx=mk[g[p][i].yy];
}
}
void dfs(int p, int q)
{
for (auto [_,it] : g[p]) if (it!=q) dfs(it,p);
tin[p]=++VREME,kad[VREME]=p,up[0][p]=q;
}
void build(int n)
{
ff(k,1,20) fff(i,1,n) up[k][i]=up[k-1][up[k-1][i]];
}
bool ball[100005];
priority_queue<int,vector<int>,greater<int>> nonballs; //zprv ubacujemo vremena u ovaj set
int main()
{
FAST;
int n,q; cin>>n>>q;
fff(i,1,n)
{
int p; cin>>p;
if (p) g[p].pb({-1,i});
else rootcina=i;
}
cringedfs(rootcina,0);
fff(i,1,n) sort(all(g[i]));
dfs(rootcina,0);
build(n);
fff(i,1,n) nonballs.push(tin[i]);
while (q--)
{
int t,x; cin>>t>>x;
if (t==1)
{
int lst;
while (x--)
{
auto v=nonballs.top();
nonballs.pop();
lst=kad[v];
ball[lst]=true;
}
cout<<lst<<"\n";
}
else
{
int kolko=0;
bff(k,0,20) if (ball[up[k][x]]) x=up[k][x],kolko+=(1<<k);
ball[x]=false,nonballs.push(tin[x]);
cout<<kolko<<"\n";
}
}
}
//Note to self: Check for overflow
