/**
* @file msz2.cpp
* @author random(usrnm: Pekiban) z oj.uz
* @brief Wzo - O(n * logn)
*/
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define lwb lower_bound
const int N = 1e5 + 5, LOG = 17;
vector<int> g[N];
int up[LOG][N], D[N], mn[N], ps[N];
vector<int> a = {-1};
void dfs1(int s, int e = -1)
{
mn[s] = s;
for (auto u : g[s])
{
if (u == e)
continue;
D[u] = D[s] + 1;
up[0][u] = s;
dfs1(u, s);
mn[s] = min(mn[s], mn[u]);
}
}
bool cmp(int x, int y)
{
return mn[x] < mn[y];
}
void dfs2(int s, int e = -1)
{
sort(g[s].begin(), g[s].end(), cmp);
for (auto u : g[s])
{
if (u == e)
continue;
dfs2(u, s);
}
a.pb(s);
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
int n, q, R;
cin >> n >> q;
for (int i = 1; i <= n; ++i)
{
int p;
cin >> p;
if (i == 0)
{
R = i;
continue;
}
g[p].pb(i);
g[i].pb(p);
}
dfs1(R);
dfs2(R);
for (int i = 1; i < LOG; ++i)
{
for (int j = 1; j <= n; ++j)
{
up[i][j] = up[i - 1][up[i - 1][j]];
}
}
for (int i = 1; i <= n; ++i)
ps[a[i]] = i;
ps[0] = 1e9;
set<int> r, av;
for (int i = 1; i <= n; ++i)
av.insert(i);
map<int, int> L;
L[0] = 1;
while (q--)
{
int t;
cin >> t;
if (t == 1)
{
int k, ans=0;
cin >> k;
while (k--)
{
int x = *av.begin();
av.erase(x);
if (r.lwb(x) == r.end() || x + 1 < L[*r.lwb(x)])
{
L[x] = L[x - 1];
if (x > 1)
L.erase(x - 1);
if (x > 1)
r.erase(x - 1);
r.insert(x);
}
else
{
L[*r.lwb(x)] = L[x - 1];
if (x > 1)
L.erase(x - 1);
if (x > 1)
r.erase(x - 1);
}
ans = x;
}
cout << a[ans] << '\n';
}
else
{
int x;
cin >> x;
int X = x, ri = *r.lwb(ps[x]);
for (int i = LOG - 1; i >= 0; --i)
{
if (ps[up[i][x]] <= ri)
x = up[i][x];
}
L[ps[x] - 1] = L[ri];
r.insert(ps[x] - 1);
if (ps[x] - 1 < L[ps[x] - 1])
{
L.erase(ps[x] - 1);
r.erase(ps[x] - 1);
}
L[ri] = ps[x] + 1;
if (L[ri] > ri)
{
L.erase(ri);
r.erase(ri);
}
av.insert(ps[x]);
cout << D[X] - D[x] << '\n';
}
}
}
