#include<bits/stdc++.h>
#include <iomanip>
using namespace std;
#define FIO ios_base::sync_with_stdio(false);cin.tie(0);
#define ll long long
#define for_t ll T;cin>>T;while(T--)
#define endl "\n"
#define mod 1000000007
#define inf 1000000000000000001
#define all(c) c.begin(),c.end()
#define pb push_back
#define lc(curr) (curr * 2)
#define rc(curr) ((curr * 2) + 1)
const int maxn = 100005;
vector<ll> adj[maxn];
ll parent[maxn];
vector<bool> hasball(maxn,false);
ll cnt,root,last;
ll minnode[maxn];//min node in the subtree of i
vector<ll> order;
map<ll,ll> mp;
set<pair<ll,ll>> nb;//these nodes do not have balls
ll tin[maxn];
ll tout[maxn];
ll timer = 0;
ll up[maxn][35];
//find the contiguous nodes in ancestors of i that have a ball
void remnode(ll i)
{
ll cnt = 0;
ll curr = i;
for(int j = 30;j >= 0;j--)
{
if(hasball[up[curr][j]])
{
curr = up[curr][j];
cnt += pow(2,j);
}
}
hasball[curr] = false;
nb.insert({mp[curr],curr});
cout << cnt << endl;
}
bool comp(ll i,ll j)
{
return minnode[i] < minnode[j];
}
void dfs(ll i)
{
minnode[i] = i;
for(auto it:adj[i])
{
dfs(it);
minnode[i] = min(minnode[i],minnode[it]);
}
}
void dfs2(ll i)
{
for(auto it:adj[i])
{
dfs2(it);
order.pb(it);
}
order.pb(i);
mp[i] = order.size() - 1;
nb.insert({mp[i],i});
}
void lcadfs(ll i,ll parent)
{
tin[i] = timer++;
up[i][0] = parent;
for(int j = 1;j <= 30;j++)
{
up[i][j] = up[up[i][j - 1]][j - 1];
}
for(auto it:adj[i])
{
lcadfs(it,i);
}
tout[i] = timer++;
}
void sol()
{
ll n,q;
cin >> n >> q;
for(int i = 1;i <= n;i++)
{
cin >> parent[i];
if(parent[i] == 0)
{
root = i;
}
else
{
adj[parent[i]].pb(i);
}
}
dfs(root);
for(int i = 1;i <= n;i++)
{
sort(all(adj[i]),comp);
}
dfs2(root);
memset(up,0,sizeof(up));
lcadfs(root,0);
for(int i = 0;i < q;i++)
{
ll x,y;
cin >> x >> y;
if(x == 1)
{
for(int j = 0;j < y;j++)
{
ll u = (*nb.begin()).second;
hasball[u] = true;
last = u;
nb.erase(*nb.begin());
}
cout << last << endl;
}
else
{
remnode(y);
}
}
}
int main()
{
FIO
sol();
}
