#include <bits/stdc++.h>
#define all(x) (x).begin(), (x).end()
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pull;
typedef pair<int, int> pii;
typedef pair<ld, ld> pld;
int n, q;
int bit[100009];
int get(int idx){
int ret = 0;
for(++idx; idx > 0; idx -= idx&(-idx))
ret += bit[idx];
return ret;
}
void upd(int idx, int val){
for(++idx; idx <= n; idx += idx&(-idx))
bit[idx] += val;
}
void updrange(int l, int r, int val){
upd(l, val);
upd(r+1, -val);
}
int val[100009];
vector<int> g[100009];
int root;
int dad[100009][20];
void dfs1(int v){
for(int i = 1; i < 20; ++i)
dad[v][i] = dad[dad[v][i-1]][i-1];
for(auto u : g[v]){
dad[u][0] = v;
dfs1(u);
val[v] = min(val[v], val[u]);
}
}
int sf(int x, int y){
return val[x] < val[y];
}
int tin[100009];
int tout[100009];
int ord[100009];
int curtime = 0;
int curord = 0;
void dfs2(int v){
sort(all(g[v]), sf);
tin[v] = curtime++;
for(auto u : g[v]){
dfs2(u);
}
tout[v] = curtime-1;
ord[v] = curord++;
}
int goup(int v, int x){
for(int i = 19; i >= 0; --i)
if(x&(1<<i))
v = dad[v][i];
return v;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
//freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
cin >> n >> q;
for(int i = 1; i <= n; ++i){
val[i] = i;
int prt;
cin >> prt;
if(prt == 0)
root = i;
else
g[prt].pb(i);
}
dfs1(root);
dfs2(root);
set<pii> s;
for(int i = 1; i <= n; ++i)
s.insert({ord[i], i});
while(q--){
int t, k;
cin >> t >> k;
if(t == 1){
int last;
while(k--){
last = s.begin()->ss;
s.erase(s.begin());
updrange(tin[last], tout[last], 1);
}
cout << last << '\n';
}
else{
int rolldown = get(tin[k])-1;
cout << rolldown << '\n';
int v = goup(k, rolldown);
s.insert({ord[v], v});
updrange(tin[v], tout[v], -1);
}
}
}
