#include <bits/stdc++.h>
#define fr(i, n, m) for(int i = (n); i < (m); i ++)
#define pb push_back
#define st first
#define nd second
#define pq priority_queue
#define all(x) begin(x), end(x)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const ll inf = 1e18;
const int i_inf = 1e9;
const ll mod = 1e9+7;
mt19937 _rand(time(NULL));
const int mxn = 1e5+5;
vector<int> g[mxn];
int n, q;
int dep[mxn];
int sparse[mxn][20];
int mi[mxn][20];
int sub[mxn];
int msub[mxn];
int t_p = 1;
int eul[mxn];
int ieul[mxn];
void dfs(int u, int p){
ieul[t_p] = u;
eul[u] = t_p++;
sparse[u][0] = p;
fr(i, 1, 20) sparse[u][i] = sparse[sparse[u][i-1]][i-1];
mi[u][0] = min(u, p);
fr(i, 1, 20){
mi[u][i] = min(mi[u][i-1], mi[sparse[u][i-1]][i-1]);
}
msub[u] = u;
sub[u] = 1;
for(auto e : g[u]){
dep[e] = dep[u]+1;
dfs(e, u);
msub[u] = min(msub[u], msub[e]);
sub[u] += sub[e];
}
}
int lca(int a, int b){
int d = min(dep[a], dep[b]);
for(int i = 19; i >= 0; i --){
if(dep[a] - (1<<i) >= d){
a = sparse[a][i];
}
if(dep[b] - (1<<i) >= d){
b = sparse[b][i];
}
}
if(a == b) return a;
for(int i = 19; i >= 0; i --){
if(sparse[a][i] != sparse[b][i]){
a = sparse[a][i];
b = sparse[b][i];
}
}
return sparse[a][0];
}
int path(int u, int p){
int ret = n;
for(int i = 19; i >= 0; i--){
if(dep[u] - (1<<i) > dep[p]){
ret = min(ret, mi[u][i]);
u = sparse[u][i];
}
}
return ret;
}
bool cmp(int a, int b){
int c = lca(a, b);
if(b == c) return true;
else if(a == c) return false;
else{
int m1 = min(path(a, c), msub[a]);
int m2 = min(path(b, c), msub[b]);
return m1 < m2;
}
}
vector<int> v;
int bit[mxn];
void update(int k, int v){
while(k <= n){
bit[k] += v;
k += k&-k;
}
}
int findpos(){
int k = 0;
int sum = 0;
for(int i = 19; i >= 0; i --){
if(k + (1<<i) <= n && sum + bit[k+(1<<i)] == k+(1<<i)){
k += (1<<i);
sum += bit[k];
}
}
return k + 1;
}
int pos[mxn];
int bit2[mxn];
void update2(int k, int v){
while(k <= n){
bit2[k] += v;
k += k&-k;
}
}
int sum(int k){
int ret = 0;
while(k > 0){
ret += bit2[k];
k -= k&-k;
}
return ret;
}
void solve(){
cin >> n >> q;
fr(i, 0, n){
int x;
cin >> x;
if(x == 0) continue;
g[x-1].pb(i);
}
dfs(0, 0);
fr(i, 0, n) v.pb(i);
sort(all(v), cmp);
fr(i, 0, n) pos[v[i]] = i+1;
fr(i, 0, q){
char t;
int x;
cin >> t >> x;
if(t == '1'){
int o;
fr(i, 0, x){
int p = findpos();
update(p, +1);
int node = v[p-1];
update2(eul[node], +1);
update2(eul[node]+sub[node], -1);
o = p;
}
cout<<v[o-1]+1<<endl;
}
else{
--x;
int D = sum(eul[x]);
for(int i = 19; i >= 0; i--){
if(D - 1 - (1<<i) >= 0){
x = sparse[x][i];
}
}
cout<<D-1<<endl;
update(pos[x], -1);
update2(eul[x], -1);
update2(eul[x]+sub[x], +1);
}
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
solve();
}
