#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef pair<int, int> pi;
#define debug(x) cerr << #x << ": " << x << endl
#define debug2(x, y) debug(x), debug(y)
#define repn(i, a, b) for(int i = (int)(a); i < (int)(b); i++)
#define rep(i, a) for(int i = 0; i < (int)(a); i++)
#define all(v) v.begin(), v.end()
#define mp make_pair
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define fi first
#define se second
#define sq(x) ((x) * (x))
#define inf 0x3f3f3f3f
const int mxN = 1e5 + 5;
template<class T> T gcd(T a, T b){ return ((b == 0) ? a : gcd(b, a % b)); }
int n, le;
int ind[mxN], mn[mxN], vis[mxN];
int st[mxN], fin[mxN], dep[mxN];
int num = 0, rt = -1;
vi g[mxN];
vector<vi> up;
void dfs0(int cur, int prev, int d = 0){
mn[cur] = cur;
dep[cur] = d;
for(int x : g[cur]) if(x != prev){
dfs0(x, cur, d + 1);
mn[cur] = min(mn[cur], mn[x]);
}
}
bool cmp(int a, int b){
return mn[a] < mn[b];
}
vi ord;
void dfs1(int cur, int prev){
for(int x : g[cur]) if(x != prev) dfs1(x, cur);
ord.pb(cur);
}
void dfs(int cur, int prev = rt){
st[cur] = num++;
up[cur][0] = prev;
repn(i, 1, le + 1) up[cur][i] = up[up[cur][i - 1]][i - 1];
for(int x : g[cur]) if(x != prev) dfs(x, cur);
fin[cur] = num++;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
//freopen("input.in", "r", stdin);
//freopen("output.out", "w", stdout);
int n, q;
cin >> n >> q;
memset(mn, inf, sizeof(mn));
rep(i, n){
int a;
cin >> a;
a--;
if(a >= 0){
g[i].pb(a);
g[a].pb(i);
}
else rt = i;
}
dfs0(rt, -1); //get the minimums
rep(i, n) sort(all(g[i]), cmp);
dfs1(rt, -1);
rep(i, n) ind[ord[i]] = i;
//now we have a set in which we maintain the minumum we can put smth into
//so once we get the type 1 operation, we keep putting to the min
//and erasing the first one
set<pi> st;
rep(i, n) st.insert({ind[i], i}); //we sort by the index from the toposort
up.resize(n);
le = 1;
while((1 << le) <= n) le++;
rep(i, n) up[i].resize(le + 1);
dfs(rt);
rep(i, q){
int t;
cin >> t;
if(t == 1){
int k;
cin >> k;
int lst = -1;
rep(j, k){
assert(st.size());
pi cur = *st.begin();
st.erase(st.begin());
vis[cur.se] = 1;
lst = cur.se;
}
assert(lst != -1);
cout << lst + 1 << '\n';
}
else{
//we use binary search + binary lifting
//to find the first unvisited node above the deleted one
int x;
cin >> x;
x--;
if(x == rt || !vis[up[x][0]]){
cout << 0 << '\n';
vis[x] = 0;
st.insert({ind[x], x});
continue;
}
int l = 1, r = dep[x];
while(l < r){
//we are searching for
int mid = (l + r) / 2;
int nd = x;
rep(j, le + 1) if(mid & (1 << j)) nd = up[nd][j];
if(!vis[nd]) r = mid;
else l = mid + 1;
}
//we clear the one right below the nd actually
int cur = l;
int nd = x;
/*
cout << "====" << endl;
rep(j, n) cout << vis[j] << " ";
cout << endl;
cout << "====" << endl;
*/
rep(j, le + 1) if(cur & (1 << j)) nd = up[nd][j];
//debug(nd);
//debug(vis[nd]);
//assert(vis[nd] && !vis[up[nd][0]]);
if(!vis[nd]){
cur--;
nd = x;
l--;
rep(j, le + 1) if(cur & (1 << j)) nd = up[nd][j];
assert(vis[nd]);
}
vis[nd] = 0;
st.insert({ind[nd], nd});
cout << l << '\n';
}
}
return 0;
}
/*
Things to look out for:
- Integer overflows
- Array bounds
- Special cases
Be careful!
*/
