#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
typedef tree<int,null_type,less<int>,rb_tree_tag,
tree_order_statistics_node_update> indexed_set;
typedef long long ll;
typedef long double ld;
///#define int ll
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<ld,ld> pld;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
#define pb push_back
#define popb pop_back
#define pp pop_back
#define pf push_front
#define popf pop_front
#define all(x) (x).begin(),(x).end()
#define ff first
#define ss second
int nx[4] = {0,0,1,-1}, ny[4] = {1,-1,0,0};
ll gcd(ll a , ll b) {return b ? gcd(b , a % b) : a ;}
ll lcm(ll a , ll b) {return (a * b) / gcd(a , b);}
const ll MOD = 998244353;
const int nax = 1e5 + 4;
int n, q;
vi adj[nax];
int sp[nax][20], d[nax], mini[nax];
int root = 1;
void dfs(int x, int p)
{
d[x] = d[p] + 1;
sp[x][0] = p;
mini[x] = x;
for(auto e: adj[x])
{
if(e != p)
{
dfs(e,x);
mini[x] = min(mini[x], mini[e]);
}
}
}
void build()
{
for(int j= 1; j < 20; j ++)
for(int i= 1 ; i <= n ;i ++)
sp[i][j] = sp[sp[i][j - 1]][j - 1];
}
int jump(int a, int k)
{
for(int i = 0; i < 20; i ++)
if((1 << i) & k)
a = sp[a][i];
return a;
}
bool comp(int a, int b)
{
if(d[a] > d[b] && jump(a, d[a] - d[b]) == b)
return true;
if(d[b] > d[a] && jump(b, d[b] - d[a]) == a)
return false;
if(mini[a] < mini[b])
return true;
else
return false;
}
void solve()
{
cin >> n >> q;
for(int i= 1; i <= n ;i ++)
{
int x; cin >> x;
if(x == 0)
root = i;
else
{
adj[x].pb(i);
adj[i].pb(x);
}
}
d[0] = -1;
dfs(root,0);
build();
vi nodes;
for(int i= 1; i <= n ;i ++)
nodes.pb(i);
sort(all(nodes),comp);
set<int> s;
for(int i = 0; i < n; i ++)
s.insert(i);
int cor[n + 1];
for(int i = 0; i < n ; i ++)
cor[nodes[i]] = i;
while(q--)
{
int type;
cin >> type;
if(type == 1)
{
int k; cin >> k;
for(int i = 1;i < k; i ++)
s.erase(s.begin());
int idx = *(s.begin());
cout << nodes[idx] << '\n';
s.erase(s.begin());
}
else
{
int x; cin >> x;
int debut = 1;
int fin = d[x];
int rep = 0;
while(debut <= fin)
{
int mid = (debut + fin)/2;
if(s.count(cor[jump(x,mid)]) == 0)
{
rep = mid;
debut= mid + 1;
}
else
fin = mid - 1;
}
s.insert(cor[jump(x,rep)]);
cout << rep << '\n';
}
}
}
int32_t main()
{
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
int tt = 1; //cin >> tt;
while(tt --)
solve();
}
