#include <bits/stdc++.h>
#define FOR(i, begin, end) for(int i = (begin); i < (end); i++)
#define FAST_IO ios_base::sync_with_stdio(false); cin.tie(nullptr)
#define TSTS int ttt; cin >> ttt; while(ttt--) solve()
#define F first
#define S second
#define PB push_back
#define MP make_pair
using namespace std;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long double, long double> pff;
typedef map<int, int> mii;
typedef vector<int> vi;
typedef long double ld;
typedef long long ll;
const int INF=1e9, MOD=1e9+7;
void setIO()
{
FAST_IO;
}
void setIO(string s)
{
FAST_IO;
freopen((s+".in").c_str(), "r", stdin);
freopen((s+".out").c_str(), "w", stdout);
}
const int N=1e5+10, L=28;
int n, q, p[N][L], mn[N], dp[N];
vi ad[N];
void mini(int u, int pst)
{
mn[u]=u;
for(auto x : ad[u]){
if(x==pst) continue;
mini(x, u);
mn[u]=min(mn[u], mn[x]);
}
}
void bdp(int u, int pst)
{
for(auto x : ad[u]){
if(x==pst) continue;
dp[x]=dp[u]+1;
bdp(x, u);
}
}
void ord(int u)
{
vector<pii> inf;
for(auto x : ad[u]){
inf.PB({mn[x], x});
}
sort(inf.begin(), inf.end());
ad[u].clear();
for(auto[x, y] : inf){
ad[u].PB(y);
}
}
int in;
mii c;
priority_queue<pii, vector<pii>, greater<pii>> pq;
bool is[N];
void dfs(int u, int pst)
{
for(auto x : ad[u]){
if(x==pst) continue;
dfs(x, u);
}
c[u]=++in;
pq.push({in, u});
}
void build()
{
FOR(i, 1, L)
{
FOR(j, 0, n)
{
p[j][i]=p[p[j][i-1]][i-1];
}
}
}
int lift(int x, int d)
{
FOR(i, 0, L) if(d&(1<<i)) x=p[x][i];
return x;
}
int fnd(int x)
{
int l=0, r=dp[x];
while(l<r){
int m=(l+r+1)/2;
if(!is[lift(x, m)]) r=m-1;
else l=m;
}
return l;
}
int main()
{
setIO();
cin >> n >> q;
int rt;
FOR(i, 0, n)
{
int x; cin >> x; x--;
x==-1?x=i,rt=i:x=x;
p[i][0]=x;
if(x!=i){
ad[x].PB(i);
ad[i].PB(x);
}
}
build();
mini(rt, -1);
FOR(i, 0, n) ord(i);
dfs(rt, -1);
bdp(rt, -1);
while(q--){
int t; cin >> t;
if(t==1){
int k; cin >> k;
FOR(i, 0, k-1)
{
int u=pq.top().S; pq.pop();
is[u]=true;
}
int u=pq.top().S; pq.pop();
is[u]=true;
cout << u+1 << '\n';
}
else{
int x; cin >> x; x--;
int l=fnd(x), u=lift(x, l);
cout << l << '\n';
is[u]=false;
pq.push({c[u], u});
}
}
}
