#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define X first
#define Y second
//const ll mod = 1000000007;
const ll mod = 998244353;
vector<vector<ll>> g, up;
vector<ll> mn;
ll K = 20;
void dfs0(ll u)
{
mn[u] = u;
for (ll j=1;j<K;j++)
{
up[u][j] = up[up[u][j-1]][j-1];
}
for (ll v: g[u])
{
dfs0(v);
mn[u] = min(mn[u],mn[v]);
}
}
vector<ll> Q;
void dfs(ll u)
{
vector<pair<ll,ll>> ord;
for (ll v: g[u])
{
ord.push_back({mn[v],v});
}
sort(ord.begin(),ord.end());
for (auto x: ord) dfs(x.Y);
Q.push_back(u);
}
void solve()
{
ll n, q;
cin >> n >> q;
g.resize(n+1);
mn.resize(n+1);
up.resize(n+1,vector<ll>(K));
for (ll i=1;i<=n;i++)
{
ll x;
cin >> x;
up[i][0] = x;
g[x].push_back(i);
}
dfs0(0);
dfs(0);
vector<ll> Q2(n+1);
for (ll i=0;i<=n;i++) Q2[Q[i]] = i;
set<ll> kek;
for (ll i=0;i<=n;i++) kek.insert(i);
vector<ll> was(n+1);
while (q--)
{
ll t;
ll x;
cin >> t >> x;
if (t==1)
{
ll L = 0;
while (x--)
{
L = *kek.begin();
kek.erase(L);
was[Q[L]] = 1;
}
cout << Q[L] << "\n";
continue;
}
ll A = 0;
for (ll j=K-1;j>=0;j--)
{
if (was[up[x][j]]==1)
{
A += (1LL<<j);
x = up[x][j];
}
}
cout << A << "\n";
was[x] = 0;
kek.insert(Q2[x]);
}
}
int main()
{
ios_base::sync_with_stdio(false);
ll T;
T = 1;
//cin >> T;
while (T--) solve();
}
