#include<bits/stdc++.h>
using namespace std;
#define int long long
#define F first
#define S second
#define pii pair<int, int>
#define pb push_back
#define pp pop_back
#define all(x) x.begin(), x.end()
const int N = 1e5 + 12, M = 20;
vector<int> g[N];
int n, q, t, f[N], p[N], par[M][N], root, d[N], seg[4 * N], lazy[4 * N], ls[4 * N], h[N];
pii pl[4 * N];
void ip() {
cin >> n >> q;
for (int i = 0; i < n; i++) {
int u;
cin >> u;
u--;
par[0][i] = u;
if (u == -1)
root = i;
else {
g[u].pb(i);
g[i].pb(u);
}
}
par[0][root] = root;
}
void dfs1(int u) {
d[u] = u;
for (auto i: g[u])
if (i != par[0][u]) {
h[i] = h[u] + 1;
dfs1(i);
d[u] = min(d[u], d[i]);
}
}
void dfs2(int u) {
vector<pii> tmp;
for (auto i: g[u])
if (i != par[0][u])
tmp.pb({d[i], i});
sort(all(tmp));
for (auto i: tmp)
dfs2(i.S);
f[t] = u;
p[u] = t;
t++;
}
void pre() {
dfs1(root);
dfs2(root);
for (int i = 1; i < M; i++)
for (int j = 0; j < n; j++)
par[i][j] = par[i - 1][par[i - 1][j]];
}
void shift(int id) {
if (ls[id * 2] < ls[id]) {
seg[id * 2] = lazy[id] * (pl[id * 2].S - pl[id * 2].F);
lazy[id * 2] = lazy[id];
ls[id * 2] = ls[id];
}
if (ls[id * 2 + 1] < ls[id]) {
lazy[id * 2 + 1] = lazy[id];
seg[id * 2 + 1] = lazy[id] * (pl[id * 2 + 1].S - pl[id * 2 + 1].F);
ls[id * 2 + 1] = ls[id];
}
}
void add(int l, int r, int x, int w, int id = 1) {
if (l <= pl[id].F && r >= pl[id].S) {
lazy[id] = x;
seg[id] = x * (pl[id].S - pl[id].F);
ls[id] = w;
return;
}
if (r <= pl[id].F || l >= pl[id].S)
return;
shift(id);
add(l, r, x, w, id * 2);
add(l, r, x, w, id * 2 + 1);
seg[id] = seg[id * 2] + seg[id * 2 + 1];
}
int ask(int l, int r, int id = 1) {
if (l <= pl[id].F && r >= pl[id].S)
return seg[id];
if (r <= pl[id].F || l >= pl[id].S)
return 0;
shift(id);
int res = ask(l, r, id * 2) + ask(l, r, id * 2 + 1);
seg[id] = seg[id * 2] + seg[id * 2 + 1];
return res;
}
void query() {
int w = 1;
pl[1] = {0, n};
for (int i = 1; i < 2 * n; i++) {
int mid = (pl[i].F + pl[i].S) / 2;
pl[i * 2] = {pl[i].F, mid};
pl[i * 2 + 1] = {mid, pl[i].S};
}
while (q--) {
int u, v;
cin >> u >> v;
if (u == 1) {
int l = -1, r = n;
while (r - l > 1) {
int mid = (l + r) / 2;
if (mid + 1 - ask(0, mid + 1) < v)
l = mid;
else
r = mid;
}
cout << f[r] + 1 << '\n';
add(0, r + 1, 1, w++);
}
else {
v--;
int z = v;
for (int i = M - 1; ~i; i--)
if (ask(p[par[i][v]], p[par[i][v]] + 1))
v = par[i][v];
cout << h[z] - h[v] << '\n';
add(p[v], p[v] + 1, 0, w++);
}
}
}
int32_t main() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
ip(), pre(), query();
return 0;
}
