#include <bits/stdc++.h>
#define _CRT_SECURE_NO_WARNINGS
using namespace std;
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define uniq(x) x.resize(unique(all(x)) - x.begin());
#define sort_uniq(x) sort(all(x)), uniq(x);
#define ll long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
#define V vector
#define V2dll V<V<ll>>
#define V2dint V<V<int>>
#define V2dchar V<V<char>>
#define V2dbool V<V<bool>>
#define V3dll V<V<V<ll>>>
#define V3dint V<V<V<int>>>
#define V3dchar V<V<V<char>>>
#define lb lower_bound
#define ub upper_bound
#define pb push_back
#define eb emplace_back
#define FASTIO ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
#define INF INT32_MAX
#define blt __builtin_popcount
#define clr(x) x.clear()
#define ff first
#define ss second
#define popf pop_front
#define popb pop_back
#define sz(x) int(x.size())
#define rep(a, b, c, d) for (int a = b; a <= c; a += d)
#define repl(a, b, c, d) for (int a = b; a >= c; a -= d)
mt19937_64 rng(chrono::steady_clock().now().time_since_epoch().count());
const int LG = 18;
const int N = 1e5 + 5;
int root, n;
V<int> adj[N];
int up[N][LG + 1];
int subt[N], pos[N], d[N];
bool ng[N];
V<int> order;
void dfs(int node, int p) {
subt[node] = node;
for (auto i : adj[node]) if (i != p) {
dfs(i, node); // FIXED
subt[node] = min(subt[node], subt[i]);
}
V<pii> cur;
for (auto i : adj[node]) if (i != p)
cur.pb({subt[i], i});
sort(all(cur));
V<int> tmp;
for (auto [_, v] : cur)
tmp.pb(v);
if (node != root)
tmp.pb(p);
adj[node] = tmp;
}
void dfs_order(int node, int p) {
for (auto i : adj[node]) if (i != p)
dfs_order(i, node);
order.pb(node);
}
void dfs_blift(int node, int p) {
up[node][0] = p;
rep(i, 1, LG, 1)
up[node][i] = up[up[node][i - 1]][i - 1];
for (auto i : adj[node]) if (i != p)
d[i] = d[node] + 1, dfs_blift(i, node);
}
int main()
{
FASTIO
int q;
cin >> n >> q;
rep(i, 1, n, 1) {
int x; cin >> x;
if (x == 0)
root = i;
else {
adj[i].pb(x);
adj[x].pb(i);
}
}
order = {-1};
dfs(root, root);
dfs_order(root, root);
d[root] = 1;
dfs_blift(root, root);
rep(i, 1, n, 1)
pos[order[i]] = i;
set<pii> black, white;
rep(i, 1, n, 1) {
white.insert({pos[i], i});
ng[i] = false;
//cout << d[i] << " ";
}
while (q--) {
int t; cin >> t;
if (t == 1) {
int k; cin >> k;
while (k--) {
auto it = white.begin();
auto [bs, x] = *it;
ng[x] = true;
white.erase(it);
black.insert({bs, x});
if (k == 0)
cout << x << "\n";
}
}
else {
int node; cin >> node;
int ans = d[node];
repl(i, LG, 0, 1) {
if (ng[up[node][i]]) {
node = up[node][i];
}
}
//cout << "!!!!!!!" << node << endl;
ans -= d[node];
cout << ans << "\n";
ng[node] = false;
white.insert({pos[node], node});
black.erase({pos[node], node});
}
}
}
