#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 = 22;
void solve() {
int n, q;
cin >> n >> q;
vi par(n);
for (int &x : par)
cin >> x, x--;
int root = find(all(par), -1) - par.begin();
vvi child(n);
for (int i = 0; i < n; i++)
if (i != root)
child[par[i]].push_back(i);
vi mn_subtree(n, INF);
vi depth(n, -1);
depth[root] = 0;
function<void(int, int)> f = [&](int u, int p) {
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]);
}
};
f(root, -1);
vvi up(MAXLG, vi(n, -1));
up[0] = par;
for (int j = 1; j < MAXLG; j++)
for (int i = 0; i < n; i++)
if (up[j - 1][i] != -1)
up[j][i] = up[j - 1][up[j - 1][i]];
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) {
auto [x, y] = just_lca(u, v);
return mn_subtree[x] < mn_subtree[y];
};
set<int, decltype(s_cmp)> s(s_cmp);
for (int i = 0; i < n; i++)
if (child[i].empty())
s.insert(i);
// cerr << s << "\n";
vb is_ball(n);
vi cnt_cball(n);
while (q--) {
int t, x;
cin >> t >> x;
if (t == 1) {
// cerr << "Type 1!\n";
for (int i = 1; i <= x; i++) {
// cerr << "\tIter " << i << ":\n";
// cerr << "\t\tS: " << s << "\n";
auto u = *s.begin();
s.erase(s.begin());
is_ball[u] = 1;
if (u != root) {
if (++cnt_cball[par[u]] == child[par[u]].size())
s.insert(par[u]);
}
if (i == x)
cout << u + 1 << "\n";
}
} else {
x--;
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++;
}
s.insert(x);
cout << res << "\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;
}
