#include <iostream>
#include <cstdio>
#include <vector>
#include <queue>
#include <cmath>
#include <algorithm>
#include <cstring>
using namespace std;
int n, q, root, timer=0;
bool ball[100015];
int p[25][100015], r[100015], h[100015];
pair<int, int> info[100015];
vector<int> g[100015];
priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > heap;
void Input()
{
memset(p, -1, sizeof p);
cin >> n >> q;
for (int i=1, x; i<=n; ++i)
{
cin >> x;
g[x].push_back(i);
p[0][i]=x;
}
}
void dfs(int u)
{
r[u]=u;
for (int i=0; i<(int)g[u].size(); ++i)
{
h[g[u][i]]=h[u]+1;
dfs(g[u][i]);
r[u]=min(r[u], r[g[u][i]]);
}
}
void enqueue(int u)
{
vector<pair<int, int> > a;
for (int i=0; i<(int)g[u].size(); ++i)
a.push_back({r[g[u][i]], g[u][i]});
sort(a.begin(), a.end());
for (int i=0; i<(int)a.size(); ++i)
enqueue(a[i].second);
heap.push({++timer, u});
info[u]={timer, u};
}
void Solve()
{
h[0]=0;
dfs(0);
enqueue(0);
for (int i=1; (1<<i)<=n; ++i)
for (int u=1; u<=n; ++u)
if (p[i-1][u]!=-1)
p[i][u]=p[i-1][p[i-1][u]];
for (; q; --q)
{
int t, x;
cin >> t >> x;
if (t==1)
{
for (int i=0; i<x; ++i)
{
if (i==x-1) cout << heap.top().second << '\n';
ball[heap.top().second]=true;
heap.pop();
}
} else
{
int u=x;
for (int i=log2(h[u]); i>=0; --i)
if (p[i][x]!=-1 && ball[p[i][x]]) x=p[i][x];
ball[x]=false;
heap.push(info[x]);
cout << h[u]-h[x] << '\n';
}
}
}
int main()
{
ios_base::sync_with_stdio(false); cin.tie(0);
//freopen("ball.inp", "r", stdin);
//freopen("ball.out", "w", stdout);
Input();
Solve();
}
