#include<bits/stdc++.h>
using namespace std;
const int N = 100005;
int n, q, ts, P[N], H[N], rev[N], st[N], fn[N], mn[N];
vector < int > Adj[N];
set < int > S;
struct CMPH {
inline bool operator () (int v, int u) {
return (H[v] > H[u]);
}
};
set < int , CMPH > T[N * 2];
bool CMP(int i, int j)
{
return (mn[i] < mn[j]);
}
bool CMP2(int i, int j)
{
return (st[i] < st[j]);
}
void DFS(int v)
{
mn[v] = v;
st[v] = ts ++;
for (int &u : Adj[v])
{
H[u] = H[v] + 1;
DFS(u);
mn[v] = min(mn[v], mn[u]);
}
fn[v] = ts;
}
void DFS2(int v)
{
for (int &u : Adj[v])
DFS2(u);
P[v] = ts ++;
rev[P[v]] = v;
S.insert(P[v]);
}
inline void Add(int le, int ri, int v)
{
le += n + 1;
ri += n + 1;
for (; le < ri; le >>= 1, ri >>= 1)
{
if (le & 1) T[le].insert(v), le ++;
if (ri & 1) ri --, T[ri].insert(v);
}
}
inline void Del(int le, int ri, int v)
{
le += n + 1;
ri += n + 1;
for (; le < ri; le >>= 1, ri >>= 1)
{
if (le & 1) T[le].erase(v), le ++;
if (ri & 1) ri --, T[ri].erase(v);
}
}
inline int Get(int i)
{
int v = 0;
i += n + 1;
for (; i; i >>= 1)
if (H[v] < H[*T[i].begin()])
v = *T[i].begin();
return (v);
}
int main()
{
scanf("%d%d", &n, &q);
for (int i = 1, p; i <= n; i++)
scanf("%d", &p), Adj[p].push_back(i);
DFS(0);
for (int i = 0; i <= n; i++)
sort(Adj[i].begin(), Adj[i].end(), CMP);
ts = 0; DFS2(0);
for (int i = 0; i <= n; i++)
Add(st[i], fn[i], i);
for (int i = 0; i <= n; i++)
sort(Adj[i].begin(), Adj[i].end(), CMP2);
for (; q; q --)
{
int tp, v;
scanf("%d%d", &tp, &v);
if (tp == 1)
{
int u;
for (; v; v --)
{
u = rev[*S.begin()];
S.erase(S.begin());
Del(st[u], fn[u], u);
}
printf("%d\n", u);
}
else
{
int u = Get(st[v]);
int lb = upper_bound(Adj[u].begin(), Adj[u].end(), st[v], CMP2) - Adj[u].begin() - 1;
u = Adj[u][lb];
S.insert(P[u]);
Add(st[u], fn[u], u);
printf("%d\n", H[v] - H[u]);
}
}
return 0;
}
