#include<bits/stdc++.h>
typedef long long ll;
#define pii pair<ll, ll>
#define fi first
#define se second
#define endl '\n'
#define TASK "+"
#define N 100005
#define LOG 16
using namespace std;
const ll offset = 1e6, inf = 1e18;
bool ghuy4g;
struct Node {
ll sum, mn;
} st[4 * N], f[4 * N];
ll n, q, in[N], out[N], par[N][LOG + 2], timeDfs, dep[N], tour[N], root, sz[N];
vector<ll> adj[N];
bool is[N];
ll mini[N];
bool cmp(ll u, ll v) {
return mini[u] < mini[v];
}
void dfs1(ll u, ll parent) {
mini[u] = u;
for (auto v : adj[u]) {
if (v == parent) continue;
dfs1(v, u);
mini[u] = min(mini[u], mini[v]);
}
}
void dfs(ll u, ll parent) {
in[u] = ++ timeDfs;
sz[u] = 1;
tour[timeDfs] = u;
for (auto v : adj[u]) {
if (v == parent) continue;
dep[v] = dep[u] + 1;
par[v][0] = u;
dfs(v, u);
sz[u] += sz[v];
}
if (adj[u].size() == 1 && u != root) is[u] = 1;
out[u] = timeDfs;
}
Node cb(Node A, Node B) {
Node res;
res.sum = A.sum + B.sum;
res.mn = min(A.mn, B.mn);
return res;
}
void build(ll id, ll l, ll r) {
if (l == r) {
st[id] = {1, inf};
if (is[tour[l]]) {
st[id] = {1, l};
}
f[id] = {-1, -1};
return;
}
ll mid = (l + r) / 2;
build(id * 2, l, mid);
build(id * 2 + 1, mid + 1, r);
st[id] = cb(st[id * 2], st[id * 2 + 1]);
f[id] = {-1, -1};
}
void pre() {
dfs1(root, root);
for (int i = 1; i <= n; i ++) {
sort(adj[i].begin(), adj[i].end(), cmp);
}
dfs(root, root);
for (int j = 1; j <= LOG; j ++) {
for (int i = 1; i <= n; i ++) {
ll p = par[i][j - 1];
par[i][j] = par[p][j - 1];
}
}
build(1, 1, n);
}
ll kth_par(ll u, ll k) {
for (int j = LOG; j >= 0; j --) {
if (k >= (1 << j)) {
k -= (1 << j);
u = par[u][j];
}
}
return u;
}
void lazy(ll id) {
if (f[id].sum == -1) return;
st[id] = f[id];
if (id * 2 < 4 * N) f[id * 2] = f[id];
if (id * 2 + 1 < 4 * N) f[id * 2 + 1] = f[id];
f[id] = {-1, -1};
}
Node get(ll id, ll l, ll r, ll L, ll R) {
lazy(id);
if (l > R || r < L) return {0LL, inf};
if (L <= l && r <= R) return st[id];
ll mid = (l + r) / 2;
return cb(get(id * 2, l, mid, L, R), get(id * 2 + 1, mid + 1, r, L, R));
}
void update(ll id, ll l, ll r, ll L, ll R, Node v) {
lazy(id);
if (l > R || r < L) return;
if (L <= l && r <= R) {
f[id] = v;
lazy(id);
return;
}
ll mid = (l + r) / 2;
update(id * 2, l, mid, L, R, v);
update(id * 2 + 1, mid + 1, r, L, R, v);
st[id] = cb(st[id * 2], st[id * 2 + 1]);
}
void solve1(ll k) { // add k con vao
ll node = tour[st[1].mn]; // dinh u, dinh thap nhat
//cout << "bdnode " << node << endl;
//return;
ll kq = 0;
while (k) {
node = tour[st[1].mn];
ll l = 0, r = dep[node], ans = 0, ans_u = node;
Node res;
ll l2 = 0;
while (l <= r) {
ll mid = (l + r) / 2; // nhay len mid con
ll u = kth_par(node, mid);
Node xet = get(1, 1, n, in[u], out[u]);
//cout << " mid " << mid << " u " << u << " " << xet.sum << " l r " << l << " " << r << endl;
//if (l2 >= 3) break;
if (xet.sum <= k) {
ans = mid;
ans_u = u;
res = xet;
l = mid + 1;
}
else {
r = mid - 1;
}
}
//cout << " ans_u " << ans_u << " " << res.sum << endl;
// o node u bi mat het, k -= size
kq = ans_u;
k -= res.sum;
update(1, 1, n, in[ans_u], out[ans_u], {0, inf});
ll p = par[ans_u][0];
if (p) {
Node xet = get(1, 1, n, in[p], out[p]);
if (xet.sum == 1) {
update(1, 1, n, in[p], in[p], {xet.sum, in[p]}); // thanh la
}
}
if (st[1].mn < inf) {
node = tour[st[1].mn];
}
}
cout << kq << endl;
}
void solve2(ll x) { // rut bong o x, ban dau dinh hld, nhung co nxet: ko co chuyen o par[x][j] co, ma o par[x][j + 2] cung co
if (get(1, 1, n, in[x], in[x]).sum == 1) {
cout << -1 << endl;
return;
}
ll l = 0, r = dep[x], ans = -1, ans_u = -1;
while (l <= r) {
ll mid = (l + r) / 2;
ll u = kth_par(x, mid);
Node xet = get(1, 1, n, in[u], in[u]);
if (xet.sum == 0) {
ans = mid;
ans_u = u;
l = mid + 1;
}
else if (xet.sum == 1) {
r = mid - 1;
}
else {
cout << "ngu";
exit(4);
}
}
if (ans_u == -1) {
cout << "ngu2";
exit(5);
}
update(1, 1, n, in[ans_u], in[ans_u], {1, in[ans_u]}); // o u mat bong
is[ans_u] = 1; // chac chan bien thanh la
if (par[ans_u][0]) {
ll p = par[ans_u][0];
Node xet = get(1, 1, n, in[p], in[p]);
if (xet.mn == in[p]) {
update(1, 1, n, in[p], in[p], {xet.sum, inf}); // vi ko con la la
is[p] = 0;
}
}
cout << abs(dep[ans_u] - dep[x]) << endl;
}
void solve() {
for (int id = 1; id <= q; id ++) {
ll type, x;
cin >> type >> x;
if (type == 1) {
solve1(x);
}
else {
solve2(x);
}
}
}
bool klinh;
signed main() {
// freopen("test.inp", "r", stdin);
//freopen("test.out", "w", stdout);
//srand(time(0));
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> q;
for (int i = 1; i <= n; i ++) {
ll p; cin >> p;
if (p == 0) {
root = i;
}
else {
adj[i].push_back(p);
adj[p].push_back(i);
//cout << i << " " << p << endl;
}
}
pre();
solve();
cerr << fabs(&klinh - &ghuy4g) / double(1024 * 1024);
}
