#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <iomanip>
#include <array>
#include <string>
#include <algorithm>
#include <cmath>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <bitset>
#include <list>
#include <iterator>
#include <numeric>
#include <complex>
#include <utility>
#include <random>
#include <cassert>
#include <fstream>
using namespace std;
mt19937 rnd(time(nullptr));
/* -------------------- Typedefs -------------------- */
typedef int itn;
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef float fl;
typedef long double ld;
/* -------------------- Usings -------------------- */
using vi = vector<int>;
using vll = vector<ll>;
using mii = map<int, int>;
using mll = map<ll, ll>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
/* -------------------- Defines -------------------- */
#define ff first
#define ss second
#define pub push_back
#define pob pop_back
#define puf push_front
#define pof pop_front
#define mpr make_pair
#define yes cout<<"Yes\n"
#define no cout<<"No\n"
#define all(x) (x).begin(), (x).end()
#define USACO freopen("feast.in", "r", stdin); freopen("feast.out", "w", stdout);
/* -------------------- Constants -------------------- */
const int dx[8] = { -1, 0, 1, 0, -1, -1, 1, 1 };
const int dy[8] = { 0, -1, 0, 1, -1, 1, -1, 1 };
const int MAX = int(1e9 + 5);
const ll MAXL = ll(1e18) + 5ll;
const ll MOD = ll(1000000007);
const ll MOD2 = ll(998244353);
/* -------------------- Functions -------------------- */
void fastio() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
}
void precision(int x) {
cout.setf(ios::fixed | ios::showpoint);
cout.precision(x);
}
ll gcd(ll a, ll b) {
if (a == 0 || b == 0) return(max(a, b));
while (b) {
a %= b;
swap(a, b);
}
return a;
}
ll lcm(ll a, ll b) {
return a / gcd(a, b) * b;
}
ll range_sum(ll a, ll b) {
if (a > b) return 0ll;
ll dif = a - 1, cnt = b - a + 1;
ll ans = ((b - a + 1) * (b - a + 2)) / 2;
ans += ((b - a + 1) * dif);
return ans;
}
string dec_to_bin(ll a) {
string s = "";
for (ll i = a; i > 0; ) {
ll k = i % 2;
i /= 2;
char c = k + 48;
s += c;
}
if (a == 0) {
s = "0";
}
reverse(all(s));
return s;
}
ll bin_to_dec(string s) {
ll num = 0;
for (int i = 0; i < s.size(); i++) {
num *= 2ll;
num += (s[i] - '0');
}
return num;
}
ll factorial_by_mod(ll n, ll mod) {
ll ans = 1;
ll num;
for (ll i = 1; i <= n; ++i) {
num = i % mod;
ans *= num;
ans %= mod;
}
return ans;
}
bool isPrime(ll a) {
if (a == 1) return false;
for (ll i = 2; i * i <= a; i++) {
if (a % i == 0) return false;
}
return true;
}
ll binpow(ll a, ll b) {
if (!a) return 0;
ll ans = 1;
while (b) {
if (b & 1) {
ans *= a;
}
b >>= 1;
a *= a;
}
return ans;
}
ll binpow_by_mod(ll a, ll b, ll mod) {
if (!a) return 0;
ll ans = 1;
while (b) {
if (b & 1) {
ans *= a;
ans %= mod;
}
b >>= 1;
a *= a;
a %= mod;
}
return ans;
}
/* -------------------- Solution -------------------- */
const int N = 100005, M = 30;
vector<pii> g[N];
int sub[N], id[N], id_rev[N], dep[N], up[N][M], t[N * 4], lazy[N * 4], nsh[N * 4], ran[N * 4];
int n, q, root, cur, lg;
void dfs(int u) {
for (int l = 1; l <= lg; ++l) {
up[u][l] = up[up[u][l - 1]][l - 1];
}
sub[u] = u;
for (auto& to : g[u]) {
up[to.ss][0] = u;
dep[to.ss] = dep[u] + 1;
dfs(to.ss);
to.ff = sub[to.ss];
sub[u] = min(sub[u], sub[to.ss]);
}
sort(all(g[u]));
}
void dfs_order(int u) {
for (auto to : g[u]) {
dfs_order(to.ss);
}
id[u] = ++cur;
id_rev[cur] = u;
}
void push(int pos) {
if (!nsh[pos]) return;
t[2 * pos] = ran[2 * pos] * lazy[pos];
t[2 * pos + 1] = ran[2 * pos + 1] * lazy[pos];
lazy[2 * pos] = lazy[2 * pos + 1] = lazy[pos];
nsh[2 * pos] = nsh[2 * pos + 1] = 1;
nsh[pos] = 0;
}
void bld(int l = 1, int r = n, int pos = 1) {
ran[pos] = r - l + 1;
if (l == r) {
return;
}
int mid = (l + r) / 2;
bld(l, mid, 2 * pos);
bld(mid + 1, r, 2 * pos + 1);
}
int qry(int l, int r, int tl = 1, int tr = n, int pos = 1) {
if (l == tl && r == tr) {
return t[pos];
}
push(pos);
int mid = (tl + tr) / 2;
if (mid >= r) {
return qry(l, r, tl, mid, 2 * pos);
}
if (mid < l) {
return qry(l, r, mid + 1, tr, 2 * pos + 1);
}
return qry(l, mid, tl, mid, 2 * pos) + qry(mid + 1, r, mid + 1, tr, 2 * pos + 1);
}
void upd(int l, int r, int val, int tl = 1, int tr = n, int pos = 1) {
if (l == tl && r == tr) {
lazy[pos] = val;
t[pos] = ran[pos] * val;
nsh[pos] = 1;
return;
}
push(pos);
int mid = (tl + tr) / 2;
if (mid >= r) {
upd(l, r, val, tl, mid, 2 * pos);
}
else if (mid < l) {
upd(l, r, val, mid + 1, tr, 2 * pos + 1);
}
else {
upd(l, mid, val, tl, mid, 2 * pos);
upd(mid + 1, r, val, mid + 1, tr, 2 * pos + 1);
}
t[pos] = t[2 * pos] + t[2 * pos + 1];
}
int get_up(int u, int x) {
for (int l = lg; l >= 0; --l) {
if (x >= (1 << l)) {
x -= (1 << l);
u = up[u][l];
}
}
return u;
}
void slv() {
cin >> n >> q;
lg = log2(n);
for (int i = 1; i <= n; ++i) {
int x;
cin >> x;
if (x == 0) {
root = i;
continue;
}
g[x].pub({ 0,i });
}
up[root][0] = root;
dfs(root);
dfs_order(root);
bld();
while (q--) {
int type, x;
cin >> type >> x;
if (type == 1) {
int l = 1, r = n, mid, ind = 1;
while (l <= r) {
mid = (l + r) / 2;
int cnt_free = mid - qry(1, mid);
if (cnt_free > x) {
r = mid - 1;
}
else if (cnt_free == x) {
ind = mid;
r = mid - 1;
}
else {
l = mid + 1;
}
}
upd(1, ind, 1);
cout << id_rev[ind] << '\n';
continue;
}
int l = 0, r = dep[x], mid, ind = x, cnt = 0;
while (l <= r) {
mid = (l + r) / 2;
int node = get_up(x, mid);
if (qry(id[node], id[node])) {
l = mid + 1;
cnt = mid;
ind = node;
}
else {
r = mid - 1;
}
}
upd(id[ind], id[ind], 0);
cout << cnt << '\n';
}
}
void cs() {
int tstc = 1;
//cin >> tstc;
while (tstc--) {
slv();
}
}
void precalc() {
return;
}
int main() {
fastio();
precalc();
//precision(0);
cs();
return 0;
}
