#include <iostream>
#include <cassert>
#include <queue>
#include <bitset>
#include <cstring>
#include <vector>
#include <algorithm>
#include <deque>
#include <set>
#include <utility>
#include <functional>
#include <array>
using i64 = long long;
using u64 = unsigned long long;
using f64 = double;
using f80 = long double;
using namespace std;
#define ALL(x) x.begin(), x.end()
#define ShinLena cin.tie(nullptr)->sync_with_stdio(false);
#define N 200000
int root, n, q, L[N], J[N], P[N], tout[N], rv[N], timer, t[N<<1], low[N];
char lz[N];
vector<int> g[N];
inline void push(int v, int l, int r)
{
if (-1 == lz[v]) return;
t[v] = lz[v] * (r-l+1);
if (l != r)
{
int m = (l+r)/2, vl=v+1, vr=v+(m-l+1)*2;
lz[vl] = lz[vr] = lz[v];
}
lz[v] = -1;
}
int qry(int x, int y, int v = 0, int l = 0, int r = n - 1)
{
push(v, l, r);
if (y < l || r < x) return 0;
if (x <= l && r <= y) return t[v];
int m = (l+r)/2, vl =v + 1, vr=v+(m-l+1)*2;
return qry(x, y, vl, l, m) + qry(x, y, vr, m+1, r);
}
inline int qry(int u) { return qry(tout[u], tout[u]); }
void update(int x, int y, int k, int v = 0, int l = 0, int r = n - 1)
{
push(v, l, r);
if (y < l || r < x) return;
int m = (l+r)/2, vl =v + 1, vr=v+(m-l+1)*2;
if (x <= l && r <= y) {lz[v] = k; push(v, l, r); return; }
update(x, y, k, vl, l, m), update(x, y, k, vr, m+1, r);
t[v] = t[vl]+t[vr];
}
void init()
{
int Tin[N]{0}, Tout[N]{0}, timer = 0, t[N<<1]{0};
for (int i = 0; i < 2*n; ++i) t[i] = 1e9;
function<void(int)> dfs = [&](int u)
{
t[n + (Tin[u] = timer++)] = u;
for (auto v : g[u]) dfs(v);
Tout[u] = timer - 1;
};
dfs(root);
for (int i = n; i--;) t[i] = min(t[i<<1], t[i<<1|1]);
auto qry = [&](int l, int r)
{
int z{100000000};
for (l += n, r += n + 1; l < r; l >>= 1, r >>= 1)
{
if (l&1) z = min(z, t[l++]);
if (r&1) z = min(t[--r], z);
}
return z;
};
for (int i = 0; i < n; ++i) low[i] = qry(Tin[i], Tout[i]);
}
void dfs(int u)
{
for (auto v : g[u])
{
P[v] = u;
if (L[u] - L[J[u]] == L[J[u]] - L[J[J[u]]]) J[v] = J[J[u]];
else J[v] = u;
L[v] = L[u] + 1;
dfs(v);
}
rv[tout[u] = timer++] = u;
}
inline int highest(int u)
{
for (; u != P[u]; )
{
if (qry(J[u])) u = J[u];
else if (qry(P[u])) u = P[u];
else break;
}
return u;
}
int main()
{
ShinLena;
cin >> n >> q;
for (int i = 0; i < n; ++i) cin >> P[i], (P[i] ? void(g[P[i]-1].push_back(i)) : void(root = i));
init();
for (int i = 0; i < n; ++i) sort(ALL(g[i]), [](int a, int b){ return low[a]<low[b]; });
P[root] = root; J[root] = root;
dfs(root);
memset(lz, -1, sizeof lz);
for (int t, k; q--;)
{
cin >> t >> k;
if (t == 1)
{
int l = 0, r = n - 1;
while (l <= r)
{
int m = (l+r)/2;
if (m + 1 - qry(0, m) <= k) l = m + 1;
else r = m - 1;
}
cout << rv[l-1] + 1 << '\n';
update(0, l-1, 1);
}
else
{
int r = highest(k-1);
update(tout[r], tout[r], 0);
cout << L[k-1] - L[r] << '\n';
}
}
return 0;
}
