/*
ID: varunra2
LANG: C++
TASK: ballmachine
*/
#include <bits/stdc++.h>
using namespace std;
#ifdef DEBUG
#include "lib/debug.h"
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define debug_arr(...) \
cerr << "[" << #__VA_ARGS__ << "]:", debug_arr(__VA_ARGS__)
#pragma GCC diagnostic ignored "-Wsign-compare"
//#pragma GCC diagnostic ignored "-Wunused-parameter"
//#pragma GCC diagnostic ignored "-Wunused-variable"
#else
#define debug(...) 42
#endif
#define EPS 1e-9
#define IN(A, B, C) assert(B <= A && A <= C)
#define INF (int)1e9
#define MEM(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define MP make_pair
#define PB push_back
#define all(cont) cont.begin(), cont.end()
#define rall(cont) cont.end(), cont.begin()
#define x first
#define y second
const double PI = acos(-1.0);
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef map<int, int> MPII;
typedef multiset<int> MSETI;
typedef set<int> SETI;
typedef set<string> SETS;
typedef vector<int> VI;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<string> VS;
#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define trav(a, x) for (auto& a : x)
#define sz(x) (int)(x).size()
typedef pair<int, int> pii;
typedef vector<int> vi;
#pragma GCC diagnostic ignored "-Wsign-compare"
// util functions
int n, q;
const int siz = 20;
VI par;
VVI adj;
VI mn;
VI d;
VVI lca;
VI ord;
vector<bool> vis;
int root = 0;
void init() {
par.resize(n);
adj.resize(n);
mn.resize(n);
d.resize(n);
lca.resize(n);
vis.assign(n, false);
for (int i = 0; i < n; i++) {
lca[i].resize(siz);
}
}
void dfs1(int u, int v) {
lca[u][0] = v;
for (int i = 1; i < siz; i++) {
int to = lca[u][i - 1];
if (to == -1)
lca[u][i] = -1;
else
lca[u][i] = lca[to][i - 1];
}
mn[u] = u;
for (auto& x : adj[u]) {
if (x == v) continue;
d[x] = d[u] + 1;
dfs1(x, u);
mn[u] = min(mn[u], mn[x]);
}
}
void dfs2(int u, int v) {
VII frst;
trav(x, adj[u]) {
if (x == v) continue;
frst.PB(MP(mn[x], x));
}
sort(all(frst));
trav(x, frst) { dfs2(x.y, u); }
ord.PB(u);
}
int main() {
// #ifndef ONLINE_JUDGE
// freopen("ballmachine.in", "r", stdin);
// freopen("ballmachine.out", "w", stdout);
// #endif
cin.sync_with_stdio(0);
cin.tie(0);
cin >> n >> q;
init();
for (int i = 0; i < n; i++) {
cin >> par[i];
par[i]--;
}
root = min_element(all(par)) - par.begin();
for (int i = 0; i < n; i++) {
if (~par[i]) {
adj[i].PB(par[i]);
adj[par[i]].PB(i);
}
}
dfs1(root, -1);
dfs2(root, -1);
set<PII> empt;
// set<PII> use;
VI to(n);
rep(i, 0, n) { to[ord[i]] = i; }
for (int i = 0; i < n; i++) {
empt.insert(MP(i, ord[i]));
}
while (q--) {
int type;
cin >> type;
if (type == 1) {
int k;
cin >> k;
int lst;
while (k--) {
// we need to insert a ball
auto it = empt.begin();
PII cur = *it;
empt.erase(it);
lst = cur.y;
vis[lst] = true;
}
cout << lst + 1 << '\n';
} else {
int u;
cin >> u;
u--;
int ret = 0;
for (int i = siz - 1; i >= 0; i--) {
if (lca[u][i] != -1 and vis[lca[u][i]]) {
ret += (1 << i);
u = lca[u][i];
}
}
cout << ret << '\n';
vis[u] = false;
empt.insert(MP(to[u], u));
}
}
return 0;
}
