#include <bits/stdc++.h>
using namespace std;
const int nx=1e5+5, kx=17;
int n, q, x, pa[nx][kx], mn[nx], t, id[nx], rid[nx], c, lvl[nx], rt;
vector<int> d[nx];
struct segtree
{
int d[4*nx], lz[4*nx];
void pushlz(int l, int r, int i)
{
if (!lz[i]) return;
lz[i]=0;
d[i]=r-l+1;
if (l==r) return;
lz[2*i]=lz[2*i+1]=1;
}
void update(int l, int r, int i, int ql, int qr)
{
pushlz(l, r, i);
if (qr<l||r<ql) return;
if (ql<=l&&r<=qr) return lz[i]=1, pushlz(l, r, i), void();
int md=(l+r)/2;
update(l, md, 2*i, ql, qr);
update(md+1, r, 2*i+1, ql, qr);
d[i]=d[2*i]+d[2*i+1];
}
void update2(int l, int r, int i, int idx)
{
pushlz(l, r, i);
if (r<idx||idx<l) return;
if (l==r) return void(d[i]=0);
int md=(l+r)/2;
update2(l, md, 2*i, idx);
update2(md+1, r, 2*i+1, idx);
d[i]=d[2*i]+d[2*i+1];
}
int query(int l, int r, int i, int key)
{
pushlz(l, r, i);
if (l==r) return l;
int md=(l+r)/2;
if (md-l+1-d[2*i]>=key) return query(l, md, 2*i, key);
else return query(md+1, r, 2*i+1, key-(md-l+1-d[2*i]));
}
bool query2(int l, int r, int i, int idx)
{
pushlz(l, r, i);
if (idx<l||r<idx) return 0;
if (l==r) return d[i]==1;
int md=(l+r)/2;
return query2(l, md, 2*i, idx)||query2(md+1, r, 2*i+1, idx);
}
} s;
void dfs(int u, int p)
{
pa[u][0]=p; lvl[u]=lvl[p]+1;
mn[u]=u;
for (int i=1; i<kx; i++) pa[u][i]=pa[pa[u][i-1]][i-1];
for (auto v:d[u]) dfs(v, u), mn[u]=min(mn[u], mn[v]);
}
void dfs2(int u)
{
vector<pair<int, int>> tmp;
for (auto v:d[u]) tmp.push_back({mn[v], v});
sort(tmp.begin(), tmp.end());
for (auto [x, y]:tmp) dfs2(y);
id[u]=++t;
rid[t]=u;
}
int main()
{
cin.tie(NULL)->sync_with_stdio(false);
cin>>n>>q;
for (int i=1; i<=n; i++)
{
cin>>x;
if (x!=0) d[x].push_back(i);
else rt=i;
}
dfs(rt, rt); dfs2(rt);
while (q--)
{
cin>>t>>x;
if (t==1)
{
x=s.query(1, n, 1, x);
s.update(1, n, 1, 1, x);
cout<<rid[x]<<'\n';
}
else
{
int sv=x;
for (int i=kx-1; i>=0; i--) if (s.query2(1, n, 1, id[pa[x][i]])==1) x=pa[x][i];
s.update2(1, n, 1, id[x]);
cout<<lvl[sv]-lvl[x]<<'\n';
}
}
}
/*
8 9
0
1
2
2
3
3
4
6
1 8
2 5
2 7
2 8
1 3
2 8
2 8
2 8
2 8
*/
