#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e5 + 10;
vector<int> grafo[MAXN];
int Sub[MAXN];
int MinSub[MAXN];
int lift[MAXN][25];
int seg[4*MAXN], lz[4*MAXN];
int tin[MAXN], tout[MAXN];
int tmp = 0;
int nit[MAXN];
void dfs(int v)
{
// tin[v] = ++tmp;
Sub[v] = 1; MinSub[v] = v;
for (auto viz : grafo[v])
{
dfs(viz);
Sub[v] += Sub[viz];
MinSub[v] = min(MinSub[v], MinSub[viz]);
}
// tout[v] = tmp;
}
void dfsTin(int v)
{
for (auto viz : grafo[v]) dfsTin(viz);
tin[v] = ++tmp; nit[tmp] = v;
}
bool cmp(int a, int b)
{
return MinSub[a] < MinSub[b];
}
void refresh(int pos, int ini, int fim)
{
if (lz[pos] == -1) return;
seg[pos] = (fim - ini + 1) * lz[pos];
if (ini != fim)
{
int e = 2*pos; int d = 2*pos + 1;
lz[e] = lz[pos];
lz[d] = lz[pos];
}
lz[pos] = -1;
}
void update(int pos, int ini, int fim, int p, int q, int val)
{
refresh(pos, ini, fim);
if (q < ini || p > fim) return;
if (p <= ini && fim <= q)
{
lz[pos] = val;
refresh(pos, ini, fim);
return;
}
int m = (ini + fim) / 2;
int e = 2*pos; int d = 2*pos + 1;
update(e, ini, m , p, q, val);
update(d, m+1, fim, p, q, val);
seg[pos] = seg[e] + seg[d];
}
int query(int pos, int ini, int fim, int p, int q)
{
refresh(pos, ini, fim);
if (q < ini || p > fim) return 0;
if (p <= ini && fim <= q) return seg[pos];
int m = (ini + fim) / 2;
int e = 2*pos; int d = 2*pos + 1;
return query(e, ini, m, p, q) + query(d, m+1, fim, p, q);
}
int bb(int pos, int ini, int fim)
{
refresh(pos, ini, fim);
if (ini == fim) return ini;
int m = (ini + fim) / 2;
int e = 2*pos; int d = 2*pos + 1;
if ((m - ini + 1) > seg[e]) return bb(e, ini, m);
else return bb(d, m+1, fim);
}
void build(int pos, int ini, int fim)
{
seg[pos] = 0; lz[pos] = -1;
if (ini == fim) return;
int m = (ini + fim) / 2;
int e = 2*pos; int d = 2*pos + 1;
build(e, ini, m );
build(d, m+1, fim);
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int N, Q;
cin >> N >> Q;
for (int i = 1; i <= N; i++)
{
cin >> lift[i][0];
grafo[lift[i][0]].push_back(i);
}
dfs(0);
// for (int i = 1; i <= N; i++) cerr << "BABA " << i << " " << tin[i] << " " << tout[i] << '\n';
build(1, 1, N);
for (int i = 1; i <= N; i++) sort(grafo[i].begin(), grafo[i].end(), cmp);
dfsTin(0);
for (int k = 1; k <= 20; k++)
{
for (int i = 1; i <= N; i++) lift[i][k] = lift[ lift[i][k-1] ][k-1];
}
while (Q--)
{
int type;
cin >> type;
if (type == 1)
{
int K;
cin >> K;
int pos = 0;
while (K--)
{
pos = bb(1, 1, N);
update(1, 1, N, pos, pos, 1);
}
cout << nit[pos] << '\n';
}
else
{
int X;
cin >> X;
int resp = 0;
for (int k = 20; k >= 0; k--)
{
int prox = lift[X][k];
if (prox == 0) continue;
// cerr << X << " " << prox << '\n';
if (query(1, 1, N, tin[prox], tin[prox]))
{
// cerr << lift[X][k] << " esta cheio, somando " << (1 << k) << '\n';
X = prox;
resp += (1 << k);
}
}
update(1, 1, N, tin[X], tin[X], 0);
cout << resp << '\n';
}
}
}
