#include<bits/stdc++.h>
#define pll pair<ll, ll>
#define fi first
#define se second
#define pb push_back
#define pii pair<ll, pll>
using namespace std;
using ll = int;
const int N = 2e5+55;
const ll mod = 1e9+7;
const ll mod1 = 1e9+1;
const ll base = 311;
const ll base1 = 331;
ll m, n, t, k, a[N], tong, b[N], dp[N], c[N], lab[N], cnt, ans, P[N][20], h[N], d[N];
priority_queue< pll, vector<pll>, greater<pll> > pq;
string s[N];
vector<ll> adj[N];
vector<pll> e;
ll pw(ll k, ll n)
{
ll total = 1;
for(; n; n >>= 1)
{
if(n & 1)total = total * k % mod;
k = k * k % mod;
}
return total;
}
bool cmp(const ll& x, const ll& y)
{
return b[x] < b[y];
}
void dfs(ll u, ll p)
{
for(int i = 1; i <= 18; i ++)P[u][i] = P[P[u][i-1]][i-1];
b[u] = u;
for(ll v : adj[u])
{
if(v == p)continue;
P[v][0] = u;
dfs(v, u);
b[u] = min(b[u], b[v]);
}
if(p)
{
for(int i = 0; i < adj[u].size(); i ++)
{
if(adj[u][i] == p)
{
adj[u][i] = adj[u].back();
adj[u].pop_back();
break;
}
}
}
sort(adj[u].begin(), adj[u].end(), cmp);
}
void getid(ll u)
{
for(ll v : adj[u])
{
//cout << u <<" "<<v<<'\n';
h[v] = h[u] + 1;
getid(v);
}
//cout << u <<" "<<h[u]<<'\n';
d[u] = ++cnt;
}
ll par(ll u, ll dis)
{
for(int i = 18; i >= 0; i --)if((dis >> i) & 1)u = P[u][i];
return u;
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n >> m;
for(int i = 1; i <= n; i ++)
{
cin >> a[i];
if(!a[i])k = i;
else
{
adj[a[i]].pb(i);
adj[i].pb(a[i]);
}
}
//cout << k << '\n';
dfs(k, 0);
getid(k);
for(int i = 1; i <= n; i ++)pq.push({d[i], i});
while(m -- > 0)
{
ll x;
cin >> t >> x;
if(t == 1)
{
ans = 0;
while(x -- > 0)
{
ans = pq.top().se;
lab[ans] = 1;
pq.pop();
}
cout << ans << '\n';
}
else
{
ll lf = 0, rt = h[x], mid;
while(lf <= rt)
{
mid = (lf + rt) / 2;
k = par(x, mid);
if(lab[k])lf = mid + 1;
else rt = mid - 1;
}
ans = par(x, rt);
pq.push({d[ans], ans});
lab[ans] = 0;
//cout << ans << '\n';
cout << h[x] - h[ans] << '\n';
}
}
}
/*
1
5 9
1 2 3 2
1 3 2 -2
2 2 3
1 3 2 -3
2 2 3
1 1 4 7
1 4 5 8
2 5 2
2 5 1
1 5 6
1 1 2 2
1 2 4 3
2 1 4
1 1 5 6
1 2 3 -2
2 3 5
*/
