#include <algorithm>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#ifdef DEBUG
#include <time.h>
#endif
#define all(a) (a).begin(), (a).end()
#define rev(a) (a).rbegin(), (a).rend()
#define F first
#define S second
int recur_depth = 0;
#ifdef DEBUG
#define dbg(x) \
{ \
++recur_depth; \
auto x_ = x; \
--recur_depth; \
cerr << string(recur_depth, '\t') << "\e[91m" << __func__ << ":" \
<< __LINE__ << "\t" << #x << " = " << x_ << "\e[39m" << endl; \
}
#else
#define dbg(x)
#endif
using namespace std;
using namespace __gnu_pbds;
typedef pair<int, int> ii;
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> llll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<pair<int, int>> vii;
typedef vector<pair<int, ii>> viii;
typedef vector<vii> vvii;
typedef vector<viii> vviii;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<pair<ll, ll>> vll;
typedef vector<vll> vvll;
typedef vector<bool> vb;
template <class type1>
using ordered_set = tree<type1, null_type, less<type1>, rb_tree_tag,
tree_order_statistics_node_update>;
template <typename A, typename B>
ostream &operator<<(ostream &os, const pair<A, B> &p) {
return os << '(' << p.first << ", " << p.second << ')';
}
template <typename T_container, typename T = typename enable_if<
!is_same<T_container, string>::value,
typename T_container::value_type>::type>
ostream &operator<<(ostream &os, const T_container &v) {
os << '{';
string sep;
for (const T &x : v)
os << sep << x, sep = ", ";
return os << '}';
}
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
const ll INF = 1e9;
const ld EPS = 1e-9;
const int MAXLG = 18;
const int MAXN = 1e5 + 10;
int n, q, root;
int par[MAXN], mn_subtree[MAXN], depth[MAXN], tin[MAXN], tout[MAXN],
up[MAXLG][MAXN], cnt_cball[MAXN];
vi child[MAXN];
bool is_ball[MAXN], inq[MAXN];
void solve() {
cin >> n >> q;
for (int i = 0; i < n; ++i) {
cin >> par[i];
if (--par[i] == -1)
root = i;
}
for (int i = 0; i < n; ++i)
if (i != root)
child[par[i]].push_back(i);
depth[root] = 0;
int timer = 0;
function<void(int, int)> f = [&](int u, int p) {
tin[u] = ++timer;
mn_subtree[u] = u;
for (int &v : child[u]) {
depth[v] = depth[u] + 1;
f(v, u);
mn_subtree[u] = min(mn_subtree[u], mn_subtree[v]);
}
tout[u] = ++timer;
};
f(root, -1);
for (int i = 0; i < n; ++i)
up[0][i] = par[i];
for (int j = 1; j < MAXLG; ++j)
for (int i = 0; i < n; ++i) {
up[j][i] = -1;
if (up[j - 1][i] != -1)
up[j][i] = up[j - 1][up[j - 1][i]];
}
auto is_anc = [&](int u, int v) {
return tin[v] <= tin[u] && tout[u] <= tout[v];
};
auto kth_anc = [&](int u, int k) {
for (int i = MAXLG - 1; i >= 0; --i)
if (k & (1 << i)) {
u = up[i][u];
}
return u;
};
auto just_lca = [&](int u, int v) -> ii {
bool swaped = 0;
if (depth[u] < depth[v])
swaped = 1, swap(u, v);
u = kth_anc(u, depth[u] - depth[v]);
for (int i = MAXLG - 1; i >= 0; --i)
if (up[i][u] != up[i][v]) {
u = up[i][u];
v = up[i][v];
}
if (swaped)
return {v, u};
return {u, v};
};
auto s_cmp = [&](int u, int v) -> bool {
if (u == v)
return 0;
if (is_anc(u, v))
return 0;
if (is_anc(v, u))
return 1;
auto [x, y] = just_lca(u, v);
return mn_subtree[x] > mn_subtree[y];
// return mn_subtree[x] < mn_subtree[y];
};
priority_queue<int, vi, decltype(s_cmp)> s(s_cmp);
// set<int, decltype(s_cmp)> s(s_cmp);
for (int i = 0; i < n; ++i)
if (child[i].empty())
s.push(i), inq[i] = 1;
// s.insert(i);
auto print_pq = [&]() {
vi tmp;
while (s.size()) {
tmp.push_back(s.top());
s.pop();
}
cerr << tmp << "\n";
for (int x : tmp)
s.push(x);
};
// print_pq();
while (q--) {
int t, x;
cin >> t >> x;
// cerr << t << " " << x << "\n";
// // cerr << "\tIS BAll: " << is_ball << "\n";
// cerr << "\tPQ: ";
// print_pq();
if (t == 1) {
for (int i = 1; i <= x; ++i) {
// cerr << "\t\tI: " << i << "\n";
// cerr << "\t\t\tPQ: ";
// print_pq();
// cerr << "\t\t\tInq: {";
// for (int i = 0; i < n; i++)
// cerr << inq[i] << ",";
// cerr << "}\n";
// int u = s.top();
// s.pop();
// auto it = s.begin();
// int u = *it;
// s.erase(it);
int u = s.top();
s.pop();
inq[u] = 0;
// cerr << "\tU: " << u << "\n";
is_ball[u] = 1;
if (u != root) {
if (++cnt_cball[par[u]] == child[par[u]].size() && !inq[par[u]])
s.push(par[u]), inq[par[u]] = 1;
// s.insert(par[u]);
}
if (i == x)
cout << u + 1 << "\n";
}
// cerr << "\tIB:";
// for (int i = 0; i < n; i++)
// cerr << is_ball[i] << ",";
// cerr << "\n";
} else {
--x;
// cerr << "\t" << x << "\n";
// is_ball[x] = 0;
// --cnt_cball[par[x]];
// int res = 0;
// while (x != root && is_ball[par[x]]) {
// is_ball[x] = 1;
// ++cnt_cball[par[x]];
// x = par[x];
// is_ball[x] = 0;
// if (x != root)
// --cnt_cball[par[x]];
// res++;
// }
// cerr << "\t\t" << res << "\t" << x << "\n";
// cerr << "\t\t" << s.count(x) << "\n";
// s.insert(x);
// cerr << "\t\t";
// print_pq();
// if (!inq[x])
// s.push(x), inq[x] = 1;
// if (x != root) {
// auto it = s.find(par[x]);
// if (it != s.end())
// s.erase(it);
// }
int l = 1, r = depth[x], ans = 0;
while (l <= r) {
int mid = (l + r) / 2;
if (is_ball[kth_anc(x, mid)]) {
ans = mid;
l = mid + 1;
} else
r = mid - 1;
}
ans = kth_anc(x, ans);
is_ball[ans] = 0;
if (ans != root)
cnt_cball[par[ans]]--;
if (!inq[ans])
s.push(ans);
cout << depth[x] - depth[ans] << "\n";
}
// cerr << "\t" << is_ball << "\n";
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(NULL);
clock_t start = clock();
int test_cases = 1;
// cin >> test_cases;
while (test_cases--)
solve();
#ifdef DEBUG
cerr << fixed << setprecision(10)
<< "\nTime Taken: " << (double)(clock() - start) / CLOCKS_PER_SEC
<< "s\n";
#endif
return 0;
}
