#include<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<cmath>
#include<set>
#include<map>
#include<queue>
#include<stack>
#include<unordered_map>
using namespace std;
using ll = long long;
ll mod = 1e18;
ll gcd(ll a, ll b) {
if (b != 0) {
return gcd(b, a % b);
}
else return a;
}
ll lcm(ll a, ll b) {
return a * b / gcd(a, b);
}
ll pv(ll a, ll b) {
if (b == 0)return 1;
ll res = pv(a, b / 2) % mod;
if (b % 2 == 1) {
return ((res * res) % mod * a) % mod;
}
else return (res * res) % mod;
}
int n;
vector<vector<int>>gp, up;
vector<int>mn, v, seg;
void update(int l, int r, int u, int i, int x) {
if (l == r) {
seg[u] = x;
return;
}
int mid = (l + r) / 2;
if (i <= mid) {
update(l, mid, 2 * u + 1, i, x);
}
else update(mid + 1, r, 2 * u + 2, i, x);
seg[u] = min(seg[2 * u + 1], seg[2 * u + 2]);
}
int get(int l, int r, int u, int lx, int rx) {
if (l >= lx && r <= rx) {
return seg[u];
}
if (l > rx || r < lx) {
return 1e9;
}
int mid = (l + r) / 2;
int a = get(l, mid, 2 * u + 1, lx, rx), b = get(mid + 1, r, 2 * u + 2, lx, rx);
return min(a, b);
}
void dfs(int u, int p) {
//cout << u << " " << p << endl;
up[u][0] = p;
for (int i = 1; i <= 18; i++) {
if (up[u][i - 1] == -1) {
up[u][i] = -1;
}
else up[u][i] = up[up[u][i - 1]][i - 1];
}
for (int x : gp[u]) {
if (x != p) {
dfs(x, u);
mn[u] = min(mn[u], mn[x]);
}
}
}
void dfs1(int u, int p) {
int poqr = 1e9, ur = -1;
vector<pair<int,int>>ap;
for (int x : gp[u]) {
if (x != p) {
ap.push_back({ mn[x],x });
}
}
sort(ap.begin(), ap.end());
for (int i = 0; i < ap.size(); i++) {
dfs1(ap[i].second, u);
}
v.push_back(u);
}
void solve() {
int n, q; cin >> n >> q;
int s = 1;
while (s < n)s <<= 1;
seg = vector<int>(2 * s - 1);
gp = vector<vector<int>>(n);
up = vector<vector<int>>(n, vector<int>(19));
mn = vector<int>(n, 1e9);
vector<int>ind(n);
int armat = -1;
for (int i = 0; i < n; i++) {
int u; cin >> u;
mn[i] = i;
--u;
if (u >= 0) {
gp[i].push_back(u);
gp[u].push_back(i);
}
else armat = i;
}
dfs(armat, -1);
dfs1(armat, -1);
for (int i = 0; i < n; i++) {
ind[v[i]] = i;
}
vector<int>ok(n);
while (q--) {
int type; cin >> type;
if (type == 1) {
int k; cin >> k;
int verjin = -1;
while (k--) {
int l = -1, r = n;
while (l + 1 < r) {
int mid = (l + r) / 2;
int x = get(0, s - 1, 0, 0, mid);
if (x == 0) {
r = mid;
}
else l = mid;
}
update(0, s - 1, 0, r, 1);
ok[v[r]] = 1;
//cout << v[r] << " ";
verjin = v[r];
}
cout << verjin + 1 << endl;
}
else {
int x; cin >> x;
--x;
if (x == armat) {
cout << 0 << endl;
ok[x] = 0;
update(0, s - 1, 0, ind[armat], 0);
continue;
}
if (ok[up[x][0]] == 0) {
cout << 0 << endl;
ok[x] = 0;
update(0, s - 1, 0, ind[x], 0);
continue;
}
int l = -1, r = n + 1;
int pat = -1;
while (l + 1 < r) {
int mid = (l + r) / 2;
int urde = x;
for (int i = 0; i <= 17; i++) {
if (mid & (1 << i)) {
if (up[urde][i] == -1) {
urde = -1;
break;
}
urde = up[urde][i];
}
}
//cout <<"TES " << mid << " " << urde << endl;
if (urde == -1) {
r = mid;
}
else if (ok[urde] == 0) {
r = mid;
}
else {
pat = urde;
l = mid;
}
}
update(0, s - 1, 0, ind[pat], 0);
//cout << " " << pat << endl;
ok[pat] = 0;
cout << l << endl;
}
}
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(nullptr);
cout.tie(nullptr);
ll t = 1;
//cin >> t;
while (t--) {
solve();
}
}
