#include <bits/stdc++.h>
using namespace std;
#define TOF_io ios_base::sync_with_stdio(false); cin.tie(0);cout.tie(0)
#define file_io freopen("input.txt","r",stdin);freopen("output.txt","w",stdout);
#define pb push_back
#define Mp make_pair
#define F first
#define S second
#define all(x) (x).begin(), (x).end()
#define SZ(x) (int) (x).size()
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef unsigned long long int ull;
const long long inf = 2147483647, INF = 1e18;
const int md = 1e9 + 7;
const int lg = 30 + 2;
const int sq = 320;
const int N = 100 * 1000 + 5;
const int MAXN = 1000 * 1000 + 5;
int n;
int q, p;
int root, sz[N], par[lg][N];
int st[N], ind[N];
int seg[N << 2];
pii a[N];
vector<int> edges[N], vec;
set<pii> s;
bool mark[N];
void upd(int id, int s, int e, int l, int r, int x) {
if (r <= s || e <= l) return;
if (l <= s && e <= r) {
seg[id] += x;
return;
}
int mid = (s + e) / 2;
upd(2 * id, s, mid, l, r, x);
upd(2 * id + 1, mid, e, l, r, x);
}
int get(int id, int s, int e, int l, int r) {
if (r <= s || e <= l) return 0;
if (l <= s && e <= r) return seg[id];
int mid = (s + e) / 2;
return seg[id] + get(2 * id, s, mid, l, r) +
get(2 * id + 1, mid, e, l, r);
}
void dfs(int pr, int v) {
vec.pb(v);
par[0][v] = pr;
for (int d = 1; d < lg; d ++) par[d][v] = par[d - 1][par[d - 1][v]];
for (int u: edges[v]) if (u != pr) dfs(v, u);
sz[v] = 1;
for (int u: edges[v]) if (u != pr) sz[v] += sz[u];
}
void solve(int v, int l, int r) {
ind[v] = r - 1;
mark[v] = true;
for (int i = 0; i < edges[v].size(); i ++) {
int u = edges[v][i];
if (mark[u]) continue;
solve(u, l, l + sz[u]);
l += sz[u];
}
}
int main() {
TOF_io;
cin >> n >> q;
for (int i = 0, pr; i < n; i ++) {
cin >> pr, pr --;
if (pr < 0) {
root = i;
continue;
}
edges[i].pb(pr), edges[pr].pb(i);
}
for (int i = 0; i < n; i ++) sort(all(edges[i]));
dfs(0, 0);
for (int i = 0; i < n; i ++) st[vec[i]] = i;
solve(root, 0, n);
for (int i = 0; i < n; i ++) a[i].F = ind[i], a[i].S = i;
sort(a, a + n);
for (int i = 0, t, k; i < q; i ++) {
cin >> t >> k, t --;
if (t) {
k --;
int cnt = get(1, 0, n, st[k], st[k] + 1);
cnt --;
for (int d = 0; d < lg; d ++) if ((cnt >> d) & 1)
k = par[d][k];
s.insert({ind[k], k});
upd(1, 0, n, st[k], st[k] + sz[k], -1);
cout << cnt << '\n';
}
else {
int res = -1;
while (k && s.size()) {
auto cur = s.begin();
int v = (*cur).S;
upd(1, 0, n, st[v], st[v] + sz[v], 1);
s.erase(cur);
res = v, k --;
}
while (k --) {
int v = a[p].S;
upd(1, 0, n, st[v], st[v] + sz[v], 1);
res = v;
p ++;
}
cout << res + 1 << '\n';
}
}
return 0;
}
