#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#pragma region dalykai
using p32 = pair<int, int>;
using p32u = pair<uint32_t, uint32_t>;
using p64 = pair<int64_t, int64_t>;
using p64u = pair<uint64_t, uint64_t>;
using vi16 = vector<int16_t>;
using vi16u = vector<uint16_t>;
using vi32 = vector<int>;
using vi32u = vector<uint32_t>;
using vi64 = vector<int64_t>;
using vi64u = vector<uint64_t>;
using vp32 = vector<p32>;
using vp32u = vector<p32u>;
using vp64 = vector<p64>;
using vp64u = vector<p64u>;
using vvi32 = vector<vi32>;
using vvi32u = vector<vi32u>;
using vvi64 = vector<vi64>;
using vvi64u = vector<vi64u>;
using vvp32 = vector<vp32>;
using vvp32u = vector<vp32u>;
using vvp64 = vector<vp64>;
using vvp64u = vector<vp64u>;
using pf32 = pair<float, float>;
using pf64 = pair<double, double>;
using pf80 = pair<long double, long double>;
using vf32 = vector<float>;
using vf64 = vector<double>;
using vf80 = vector<long double>;
using vpf32 = vector<pf32>;
using vpf64 = vector<pf64>;
using vpf80 = vector<pf80>;
using vvf32 = vector<vf32>;
using vvf64 = vector<vf64>;
using vvf80 = vector<vf80>;
using vvpf32 = vector<vpf32>;
using vvpf64 = vector<vpf64>;
using vvpf80 = vector<vpf80>;
template <typename key, typename val>
using ord_map = tree<key, val, less<key>, rb_tree_tag,
tree_order_statistics_node_update>;
template <typename key>
using ord_set = tree<key, null_type, less<key>, rb_tree_tag,
tree_order_statistics_node_update>;
const int BUF_SZ = 1 << 15;
inline namespace fast_in
{
char buf[BUF_SZ];
int pos;
int len;
char next_char(FILE *f)
{
if (pos == len)
{
pos = 0;
len = (int)fread(buf, 1, BUF_SZ, f);
if (!len)
{
return EOF;
}
}
return buf[pos++];
}
int read_int(FILE *f)
{
int x;
char ch;
int sgn = 1;
while (!isdigit(ch = next_char(f)))
{
if (ch == '-')
{
sgn *= -1;
}
}
x = ch - '0';
while (isdigit(ch = next_char(f)))
{
x = x * 10 + (ch - '0');
}
return x * sgn;
}
}
/**
* @brief gale programos flush_out kviest!!
*/
inline namespace fast_out
{
char buf[BUF_SZ];
int pos;
void flush_out(FILE *f)
{
fwrite(buf, 1, pos, f);
pos = 0;
}
void write_char(char c, FILE *f)
{
if (pos == BUF_SZ)
{
flush_out(f);
}
buf[pos++] = c;
}
void write_int(int x, FILE *f)
{
static char num_buf[100];
if (x < 0)
{
write_char('-', f);
x *= -1;
}
int len = 0;
for (; x >= 10; x /= 10)
{
num_buf[len++] = (char)('0' + (x % 10));
}
write_char((char)('0' + x), f);
while (len)
{
write_char(num_buf[--len], f);
}
write_char('\n', f);
}
}
#pragma endregion
using filled_t = bitset<(size_t)1e5>;
void find_min(int node, vvi32 &adj, vi32 &sub_min)
{
int cur = node;
for (int i = 1; i < adj[node].size(); i++)
{
int next = adj[node][i];
find_min(next, adj, sub_min);
cur = min(cur, sub_min[next]);
}
sub_min[node] = cur;
}
void sort_adj(vvi32 &adj, vi32 &sub_min)
{
auto comp = [&sub_min](int a, int b)
{
return sub_min[a] < sub_min[b];
};
for (int i = 0; i < adj.size(); i++)
{
auto &next = adj[i];
sort(next.begin() + 1, next.end(), comp);
}
}
void find_order(int node, vvi32 &adj, vi32 &order, int &count)
{
for (int i = 1; i < adj[node].size(); i++)
{
find_order(adj[node][i], adj, order, count);
}
order[node] = count;
count++;
}
void find_up(vvi32 &up, vvi32 &adj)
{
for (size_t i = 0; i < adj.size(); i++)
{
up[i][0] = adj[i][0];
}
for (size_t power = 1; power < up[0].size(); power++)
{
for (size_t i = 0; i < adj.size(); i++)
{
if (up[i][power - 1] == -1)
{
continue;
}
up[i][power] = up[up[i][power - 1]][power - 1];
}
}
}
p32 first_filled(int node, int root, vvi32 &up, filled_t &filled)
{
if (node == root)
{
return {node, 0};
}
int anc = node;
int last = up[0].size() - 1;
int distance = 0;
for (int i = last; i >= 0; i--)
{
int cur = up[anc][i];
if (cur != -1 && filled[cur])
{
anc = cur;
distance += 1 << i;
}
}
return {anc, distance};
}
p32 remove(int node, int root, vvi32 &up, filled_t &filled)
{
p32 res = first_filled(node, root, up, filled);
filled[res.first] = false;
return res;
}
int main()
{
#ifndef _AAAAAAAAA
ios_base::sync_with_stdio(false);
cin.tie(0);
#else
freopen("ball_machine.in", "r", stdin);
#ifndef __linux__
atexit([]()
{
freopen("con", "r", stdin);
system("pause"); });
#endif
#endif
int n, q;
cin >> n >> q;
vvi32 adj(n);
int root = 0;
for (size_t i = 0; i < n; i++)
{
int parent;
cin >> parent;
parent--;
adj[i].insert(adj[i].begin(), parent);
if (parent != -1)
{
adj[parent].push_back(i);
}
else
{
root = i;
}
}
vi32 sub_min(n);
filled_t filled;
find_min(root, adj, sub_min);
sort_adj(adj, sub_min);
vvi32 up(n, vi32(int(log2(n) + 1), -1));
vi32 order(n);
int count = 0;
find_up(up, adj);
find_order(root, adj, order, count);
auto comp = [order](int a, int b)
{
return order[a] < order[b];
};
set<int, decltype(comp)> empty(comp);
for (size_t i = 0; i < n; i++)
{
empty.insert(i);
}
for (size_t query = 0; query < q; query++)
{
int type, node;
cin >> type >> node;
if (type == 1)
{
int last = -1;
auto it = empty.begin();
for (int i = 0; i < node; i++)
{
last = *it;
filled[last] = true;
it++;
}
empty.erase(empty.begin(), it);
cout << last + 1 << '\n';
}
else
{
node--;
p32 res = remove(node, root, up, filled);
empty.insert(res.first);
cout << res.second << '\n';
}
}
return 0;
}
