#include<bits/stdc++.h> //:3
using namespace std;
typedef long long ll;
#define all(a) (a).begin(), (a).end()
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define pi pair<int, int>
#define sz(x) (int)((x).size())
//#define int long long
const int dx[] = {0, 1, 0, -1};
const int dy[] = {1, 0, -1, 0};
const ll inf = 2e9;
const ll mod = 1e9 + 7;
const int N = 2e5 + 11;
const ll INF64 = 3e18 + 1;
const double eps = 1e-14;
const double PI = acos(-1);
//ifstream in(".in");
//ofstream out(".out");
int n, dp[N][25], root, mn[N], cnt[N], C, q, viz[N];
vector<int>v[N];
int dfs(int nod){
int MN = inf;
for(int it : v[nod]){
MN = min(dfs(it), MN);
}
mn[nod] = min(MN, nod);
return mn[nod];
}
void dfs2(int nod){
for(auto it : v[nod]){
dfs2(it);
}
cnt[nod] = C++;
}
void solve(){
cin >> n >> q;
for(int i = 1; i <= n; i++){
cin >> dp[i][0];
v[dp[i][0]].push_back(i);
if(dp[i][0] == 0)root = i;
}
dfs(root);
for(int i = 1; i <= n; i++){
sort(all(v[i]), [](int l, int r){
return (mn[l] < mn[r]);
});
}
dfs2(root);
for(int i = 1; i <= 20; i++){
for(int j = 1; j <= n; j++){
dp[j][i] = dp[dp[j][i - 1]][i - 1];
}
}
set<pi>s;
s.insert({inf, 0});
for(int i = 1; i <= n; i++) s.insert({cnt[i], i});
while(q--){
int type, x;
cin >> type >> x;
if(type == 1){
for(int i = 1; i <= x; i++){
if(i == x)cout << (*s.begin()).ss << '\n';
viz[(*s.begin()).ss] = 1;
s.erase(s.begin());
}
}else{
int ans = 0;
for(int i = 20; i >= 0; i--){
int p = dp[x][i];
if(p && viz[p])x = p, ans += (1 << i);
}
cout << ans << '\n';
s.insert({cnt[x], x});
viz[x] = 0;
}
}
}
int32_t main(){
ios_base :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
//cout << setprecision(6) << fixed;
int T = 1;
//cin >> T;
while(T--){
solve();
}
}
