#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
const int N = 100000;
const int LOG = 18;
int par[N+5][LOG+1];
int mnn[N+5];
vector <int> graf[N+5];
void dfs_calc(int v){
mnn[v] = v;
for(int j=1; j<=LOG; j++) par[v][j] = par[par[v][j-1]][j-1];
for(auto c : graf[v]){
dfs_calc(c);
mnn[v] = min(mnn[v], mnn[c]);
}
sort(graf[v].begin(), graf[v].end(), [](int a, int b){ return mnn[a] < mnn[b]; });
}
int gde[N+5];
int niz[N+5];
int tjm;
void dfs(int v){
for(auto c : graf[v]) dfs(c);
++tjm;
niz[tjm] = v;
gde[v] = tjm;
}
struct Segment{
int sum;
bool lazy;
} seg[4*N+5];
void propagate(int node, int l, int r){
if(!seg[node].lazy) return;
seg[node].sum = r-l+1;
if(l == r){
seg[node].lazy = 0;
return;
}
seg[node*2].lazy |= seg[node].lazy;
seg[node*2+1].lazy |= seg[node].lazy;
seg[node].lazy = 0;
}
void mrg(int node, int l, int r){
int mid = (l+r)/2;
propagate(node*2, l, mid);
propagate(node*2+1, mid+1, r);
seg[node].sum = seg[node*2].sum + seg[node*2+1].sum;
}
void upd_range(int node, int l, int r, int tl, int tr){
if(tl > r || l > tr) return;
if(tl <= l && r <= tr){
seg[node].lazy = 1;
propagate(node, l, r);
return;
}
int mid = (l+r)/2;
upd_range(node*2, l, mid, tl, tr);
upd_range(node*2+1, mid+1, r, tl, tr);
mrg(node, l, r);
}
void upd_point(int node, int l, int r, int x){
propagate(node, l, r);
if(l == r){
seg[node].sum = 0;
return;
}
int mid = (l+r)/2;
if(x <= mid) upd_point(node*2, l, mid, x);
else upd_point(node*2+1, mid+1, r, x);
mrg(node, l, r);
}
int find_first(int node, int l, int r, int k){
if(l == r) return l;
int mid = (l+r)/2;
propagate(node*2, l, mid);
propagate(node*2+1, mid+1, r);
if(mid-l+1 - seg[node*2].sum >= k) return find_first(node*2, l, mid, k);
return find_first(node*2+1, mid+1, r, k - (mid-l+1 - seg[node*2].sum));
}
int get_point(int node, int l, int r, int x){
propagate(node, l, r);
if(l == r) return seg[node].sum;
int mid = (l+r)/2;
if(x <= mid) return get_point(node*2, l, mid, x);
return get_point(node*2+1, mid+1, r, x);
}
int main(){
ios_base::sync_with_stdio(false), cin.tie(0);
cout.precision(10);
cout << fixed;
int n, qrs;
cin >> n >> qrs;
int root = 0;
for(int i=1; i<=n; i++){
cin >> par[i][0];
if(par[i][0] == 0) root = i;
else graf[par[i][0]].push_back(i);
}
dfs_calc(root);
dfs(root);
while(qrs--){
int typ;
cin >> typ;
if(typ == 1){
int cnt;
cin >> cnt;
int k = find_first(1, 1, n, cnt);
upd_range(1, 1, n, 1, k);
cout << niz[k] << "\n";
}
else{
int v;
cin >> v;
int res = 0;
for(int j=LOG; j>=0; j--) if(par[v][j] && get_point(1, 1, n, gde[par[v][j]])) res += (1 << j), v = par[v][j];
cout << res << "\n";
upd_point(1, 1, n, gde[v]);
}
}
return 0;
}
