#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
#define fastio ios::sync_with_stdio(false), cin.tie(0)
#define pb push_back
#define eb emplace_back
#define f first
#define s second
#define int long long
const int maxn = 1e5 + 5;
int dep[maxn], succ[maxn][18], in[maxn], out[maxn], dfn = 0;
vector<int> adj[maxn];
int st[maxn * 4], tag[maxn * 4], id[maxn];
int mn[maxn];
int n, q;
void dfs1(int pos){
mn[pos] = pos;
for(auto x : adj[pos]){
dfs1(x);
mn[pos] = min(mn[pos], mn[x]);
}
}
void dfs(int pos, int prev){
sort(adj[pos].begin(), adj[pos].end(), [&](int a, int b){ return mn[a] < mn[b];});
in[pos] = dfn;
succ[pos][0] = prev;
for(int i = 1; i < 18; i++) succ[pos][i] = succ[succ[pos][i - 1]][i - 1];
for(auto x : adj[pos]){
dep[x] = dep[pos] + 1;
dfs(x, pos);
}
out[pos] = dfn++;
id[out[pos]] = pos;
}
void push(int v, int l, int r){
int m = (l + r) / 2;
if(tag[v]){
st[v * 2] = (m - l + 1), tag[v * 2] = 1;
st[v * 2 + 1] = (r - m), tag[v * 2 + 1] = 1;
tag[v] = 0;
}
}
int add(int val, int v = 1, int l = 0, int r = n - 1){
// cout<<"add : "<<val<<" "<<l<<" "<<r<<"\n";
st[v] += val;
if(l == r) return l;
int m = (l + r) / 2;
push(v, l, r);
if(m - l + 1 - st[v * 2] >= val){
return add(val, v * 2, l, m);
}
else{
int lft = val - (m - l + 1 - st[v * 2]);
st[v * 2] = m - l + 1, tag[v * 2] = 1;
return add(lft, v * 2 + 1, m + 1, r);
}
}
int qry(int pos, int v = 1, int l = 0, int r = n - 1){
if(l == r) return st[v];
int m = (l + r) / 2;
push(v, l, r);
if(pos <= m) return qry(pos, v * 2, l, m);
else return qry(pos, v * 2 + 1, m + 1, r);
}
void upd(int pos, int val, int v = 1, int l = 0, int r = n - 1){
if(l == r){
// cout<<"upd : "<<pos<<" "<<val<<"\n";
st[v] += val;
return;
}
push(v, l, r);
int m = (l + r) / 2;
if(pos <= m) upd(pos, val, v * 2, l, m);
else upd(pos, val, v * 2 + 1, m + 1, r);
st[v] = st[v * 2] + st[v * 2 + 1];
}
int lift(int pos, int steps){
for(int i = 17; i >= 0; i--){
if(steps & (1 << i)) pos = succ[pos][i];
}
return pos;
}
signed main(void){
// fastio;
cin>>n>>q;
int rt = 0;
for(int i = 0; i < n; i++){
int x;
cin>>x;
if(x == 0) rt = i;
else x--, adj[x].pb(i);
}
dfs1(rt);
dfs(rt, rt);
// cout<<"out : ";
// for(int i = 0; i < n; i++) cout<<out[i]<<" ";
// cout<<"\n";
int ttl = 0;
for(int i = 0; i < q; i++){
int op, k;
cin>>op>>k;
// cout<<"ttl : "<<qry(out[0])<<"\n";
if(op == 1){
cout<<id[add(k)] + 1<<"\n";
}
else{
k--;
int l = 0, r = dep[k] + 1;
while(l + 1 < r){
int m = (l + r) / 2;
int id = lift(k, m);
// cout<<"ck : "<<id<<" "<<qry(out[id])<<"\n";
if(qry(out[id])) l = m;
else r = m;
}
cout<<l<<"\n";
int x = lift(k, l);
upd(out[x], -1);
}
}
}
