#include <bits/stdc++.h>
using namespace std;
void setup()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
struct SEGMENT_TREE
{
int tree[500000];
inline void Update(int ind, int l, int r, int x, int v)
{
if (r < x || x < l)
{
return;
}
if (l == r)
{
tree[ind] += v;
return;
}
int m = (l + r) >> 1;
Update(ind << 1, l, m, x, v);
Update(ind << 1 | 1, m + 1, r, x, v);
tree[ind] = tree[ind << 1] + tree[ind << 1 | 1];
}
inline int Get(int ind, int l, int r, int x, int y)
{
if (r < x || y < l)
{
return 0;
}
if (x <= l && r <= y)
{
return tree[ind];
}
int m = (l + r) >> 1;
return Get(ind << 1, l, m, x, y) + Get(ind << 1 | 1, m + 1, r, x, y);
}
} st;
int n, q, a, b, root;
int mn[100000], id[100000], head[100000], tail[100000], sp[20][100000], depth[100000];
vector<int> g[100000];
priority_queue<pair<int, int>> pq;
inline void DFS1(int node)
{
vector<pair<int, int>> v;
mn[node] = node;
for (int i = 1; i < 20; ++i)
{
sp[i][node] = sp[i - 1][sp[i - 1][node]];
}
for (auto &i : g[node])
{
sp[0][i] = node;
depth[i] = depth[node] + 1;
DFS1(i);
v.push_back({mn[i], i});
mn[node] = min(mn[node], mn[i]);
}
sort(v.begin(), v.end());
g[node].clear();
for (auto &i : v)
{
g[node].push_back(i.second);
}
}
inline void DFS2(int node)
{
head[node] = b++;
for (auto &i : g[node])
{
DFS2(i);
}
id[node] = a++;
tail[node] = b - 1;
pq.push({-id[node], node});
}
int main()
{
setup();
cin >> n >> q;
for (int i = 0; i < n; ++i)
{
cin >> a;
if (a == 0)
{
root = i;
}
else
{
g[a - 1].push_back(i);
}
}
a = 0;
b = 1;
sp[0][root] = root;
DFS1(root);
DFS2(root);
while (q--)
{
cin >> a >> b;
if (a == 1)
{
while (b > 0 && !pq.empty())
{
a = pq.top().second;
st.Update(1, 1, n, head[a], 1);
pq.pop();
}
cout << a + 1 << "\n";
}
else
{
b--;
a = b;
for (int i = 19, j; i >= 0; --i)
{
j = sp[i][a];
if (st.Get(1, 1, n, head[j], tail[j]) == tail[j] - head[j] + 1)
{
a = j;
}
}
st.Update(1, 1, n, head[a], -1);
pq.push({-id[a], a});
cout << depth[b] - depth[a] << "\n";
}
}
return 0;
}
