// And you curse yourself for things you never done
#include<bits/stdc++.h>
#define F first
#define S second
#define PB push_back
#define sz(s) int((s).size())
#define bit(n,k) (((n)>>(k))&1)
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const int maxn = 1e5 + 10, mod = 1e9 + 7, inf = 1e9 + 10;
bool FRE[maxn];
set<int> fre;
int mn[maxn];
vector<int> v[maxn];
int st[maxn], rst[maxn];
int sp[20][maxn];
void prep(int u){
for(int i = 1; i < 20; i++)
sp[i][u] = sp[i-1][sp[i-1][u]];
mn[u] = u;
for(int y : v[u]){
sp[0][y] = u;
prep(y);
mn[u] = min(mn[u], mn[y]);
}
sort(v[u].begin(), v[u].end(), [&](int i, int j){ return mn[i] < mn[j]; });
}
void prep2(int u){
static int C = 0;
for(int y : v[u]){
prep2(y);
}
st[u] = C;
rst[C] = u;
C++;
}
int main(){
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie();
int n, q;
cin >> n >> q;
int root = -1;
for(int i = 1; i <= n; i++){
int p;
cin >> p;
if(p == 0)
root = i;
else
v[p].PB(i);
}
st[0] = n;
FRE[n] = 1;
prep(root);
prep2(root);
for(int i = 0; i < n; i++){
fre.insert(fre.end(), i);
FRE[i] = 1;
}
while(q--){
int task;
cin >> task;
int ans = 0;
if(task == 1){
int k;
cin >> k;
while(k--){
int id = *fre.begin();
FRE[id] = 0;
fre.erase(id);
ans = rst[id];
}
}
else{
int u;
cin >> u;
for(int i = 19; i >= 0; i--){
if(FRE[ st[ sp[i][u] ] ] == 0)
u = sp[i][u], ans+= 1<<i;
}
u = st[u];
fre.insert(u);
FRE[u] = 1;
}
cout << ans << "\n";
}
return 0;
}
