#define _CRT_SECURE_NO_WARNINGS
#include<bits/stdc++.h>
#include <unordered_map>
#include <unordered_set>
#include <cassert>
#include <chrono>
#include <random>
using namespace std;
using namespace chrono;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
#define ss second
#define ff first
#define all(X) X.begin(), X.end()
#define rall(X) X.rbegin(), X.rend()
#define cinall(X) for (auto &i : (X)) cin >> i
#define printall(X) for (auto &i : (X)) cout << i << " "
#define printFromTo(cont, i, j, ch) for (int _ = i; _ <= j; _++) cout << cont[_] << ch
#define cinFromTo(cont, i, j) for (int _ = i; _ <= j; _++) cin >> cont[_]
#define fillFromTo(cont, i, j, x) for (int _ = i; _ <= j; _++) cont[_] = x;
#define pb push_back
#define sz(X) (X).size()
#define m_p make_pair
#define pii pair<int, int>
#define MAKE_UNIQUE_KEEP_ORDER(vec) do { unordered_set<decltype((vec).front())> seen; (vec).erase(remove_if((vec).begin(), (vec).end(), [&](auto &val) { if (seen.count(val)) return true; seen.insert(val); return false; }), (vec).end()); } while(0)
#define UNIQUE_SORT(vec) do { sort((vec).begin(), (vec).end()); (vec).erase(unique((vec).begin(), (vec).end()), (vec).end()); } while(0)
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
#define yes cout << "YES\n"
#define no cout << "NO\n"
#define YN(b) if(b) {yes;} else {no;}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) (lower_bound((c).begin(), (c).end(), (x)) - (c).begin())
#define UB(c, x) (upper_bound((c).begin(), (c).end(), (x)) - (c).begin())
const int N = 2.4e6 + 5;
const int LOG = 21;
const long long INFLL = 1e18;
const int INF = 5e8;
const long double epsilon = 0.000001;
const long long mod = 1e9 + 7;
int dx[] = { 1, -1, 0, 0, 1, -1, -1, 1 };
int dy[] = { 0, 0, 1, -1, 1, 1, -1, -1 };
int bx[] = { 2, 2, 1, 1, -1, -1, -2, -2 };
int by[] = { 1, -1, 2, -2, 2, -2, -1, 1 };
constexpr ll TEN[] = { 1LL,10LL,100LL,1000LL,10000LL,100000LL,1000000LL,10000000LL,100000000LL,1000000000LL,10000000000LL,100000000000LL,1000000000000LL,10000000000000LL,100000000000000LL,1000000000000000LL,10000000000000000LL,100000000000000000LL,1000000000000000000LL, };
inline long long binPowByMod(long long x, long long power, long long modx) {
long long res = 1;
long long base = x % modx;
while (power > 0) {
if (power & 1) res = (res * base) % modx;
base = (base * base) % modx;
power >>= 1;
}
return res;
}
inline ll add(ll a, ll b, ll modx) {
a %= modx; b %= modx;
a += b;
if (a >= modx) a -= modx;
return a;
}
inline ll sub(ll a, ll b, ll modx) {
a %= modx; b %= modx;
a -= b;
if (a < 0) a += modx;
return a;
}
inline ll mult(ll a, ll b, ll modx) {
a %= modx; b %= modx;
return (a * b) % modx;
}
ll fact[N];
inline long long divid(long long p, long long q, long long modx) { return mult(p % modx, binPowByMod(q, modx - 2, modx), modx); }
inline ll cnk(ll a, ll b)
{
ll ans = 1;
ans = fact[a];
ans = divid(ans, fact[b], mod);
ans = divid(ans, fact[a - b], mod);
return ans;
}
ll gcdll(ll a, ll b) { return b == 0 ? a : gcdll(b, a % b); }
ll lcmll(ll a, ll b) { return a / gcdll(a, b) * b; }
ll ceil_div(ll a, ll b) { return (a + b - 1) / b; }
bool isPrime(ll x) { if (x < 2) return false; for (ll i = 2; i * i <= x; ++i) if (x % i == 0) return false; return true; }
ll range_sum(ll a, ll b) {
ll dif = a - 1, cnt = b - a + 1;
ll ans = ((b - a + 1) * (b - a + 2)) / 2;
ans += ((b - a + 1) * dif);
return ans;
}
//void set_IO(string str = "") { if (!str.empty()) { freopen((str + ".in").c_str(), "r", stdin); freopen((str + ".out").c_str(), "w", stdout); } }
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << '"' << t << '"'; }
void _print(char t) { cerr << '\'' << t << '\''; }
void _print(double t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(unsigned long long t) { cerr << t; }
void _print(bool t) { cerr << (t ? "true" : "false"); }
template<class T> void _print(vector<T> v) { cerr << "[ "; for (auto& i : v) { _print(i); cerr << " "; } cerr << "]"; }
template<class T, size_t N> void _print(array<T, N> a) { cerr << "[ "; for (auto& i : a) { _print(i); cerr << " "; } cerr << "]"; }
template<class T> void _print(set<T> v) { cerr << "{ "; for (auto& i : v) { _print(i); cerr << " "; } cerr << "}"; }
template<class T> void _print(multiset<T> v) { cerr << "{ "; for (auto& i : v) { _print(i); cerr << " "; } cerr << "}"; }
template<class T> void _print(unordered_set<T> v) { cerr << "{ "; for (auto& i : v) { _print(i); cerr << " "; } cerr << "}"; }
template<class T, class V> void _print(map<T, V> v) { cerr << "{ "; for (auto& i : v) { _print(i.first); cerr << ":"; _print(i.second); cerr << " "; } cerr << "}"; }
template<class T, class V> void _print(unordered_map<T, V> v) { cerr << "{ "; for (auto& i : v) { _print(i.first); cerr << ":"; _print(i.second); cerr << " "; } cerr << "}"; }
template<class T, class V> void _print(pair<T, V> p) { cerr << "("; _print(p.first); cerr << ", "; _print(p.second); cerr << ")"; }
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; _print(x); cerr << endl;
#else
#define dbg(x)
#endif
//#define blt __builtin_popcount
int blt(ll a) { int ans = 0; for (int i = 0; i <= 31; i++) if (a & (1ll << i)) ans++; return ans; }
int nxt(int A, int n) { return (A + 1 > n) ? (A + 1) % n : A + 1; }
int prv(int A, int n) { if (A == 1) return n; else if (A - 1 <= n) return A - 1; else return (A - 1) % n; }
mt19937 rng(chrono::steady_clock().now().time_since_epoch().count());
mt19937 rnf(777);
const int M = 1e5 + 10;
const ll inf = 1e18 / 4;
vector<int>G[N];
int sz[N], up[N][LOG], p[N];
int root;
bool used[N];
vector<int>order;
void dfs_sz(int node)
{
sz[node] = node;
vector<pair<int, int>>vec;
for (auto i : G[node])
{
dfs_sz(i);
sz[node] = min(sz[node], sz[i]);
vec.push_back({ sz[i], i });
}
sort(all(vec));
G[node].clear();
for (auto i : vec)
{
G[node].push_back(i.ss);
}
}
void dfs_q(int node)
{
for (auto i : G[node])
{
dfs_q(i);
}
order.push_back(node);
}
void dfs(int node)
{
for (auto i : G[node])
{
up[i][0] = node;
for (int j = 1; j < LOG; j++)
{
up[i][j] = up[up[i][j - 1]][j - 1];
}
dfs(i);
}
}
void solve()
{
int n, q;
cin >> n >> q;
for (int i = 1; i <= n; i++)
{
int a;
cin >> a;
if (a == 0)root = i;
if (a != 0)
{
G[a].push_back(i);
}
}
dfs_sz(root);
dfs_q(root);
dfs(root);
set<pair<int, int>>free;
for (int i = 0; i < n; i++)
{
free.insert({ i, order[i] });
p[order[i]] = i;
}
while (q--)
{
int t;
cin >> t;
if (t == 1)
{
int k;
cin >> k;
while (k--)
{
pair<int, int>u = *free.begin();
used[u.ss] = true;
free.erase(free.begin());
if (k == 0)
{
cout << u.ss << endl;
}
}
}
else
{
int ans = 0;
int x;
cin >> x;
for (int i = LOG - 1; i >= 0; i--)
{
if (used[up[x][i]])
{
ans += (1ll << i);
x = up[x][i];
}
}
used[x] = false;
free.insert({ p[x], x });
cout << ans << endl;
}
}
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int t = 1;
//cin >> t;
int T = t;
while (t--) {
cerr << "Test " << T - t << endl;
solve();
cout << endl;
}
return 0;
}
