#include <bits/stdc++.h>
#define ll long long
#define s second
#define f first
#define pb push_back
#define left (h*2),l,(l + r)/2
#define right (h*2+1),(l+r)/2 + 1,r
#define pii pair <int,int>
using namespace std;
const int N = 1e5 + 5;
vector <int> v[N];
int ord[N],mn[N],sub[N];
int pr[N],fix[N],d[25][N],t[4*N],id[N];
int lz[4*N],dep[N];
void predfs(int x,int par){
mn[x] = x;
dep[x] = dep[par] + 1;
d[0][x] = par;
sub[x] = 1;
for (int to: v[x]){
if (to == par) continue;
predfs(to,x);
mn[x] = min(mn[x],mn[to]);
sub[x] += sub[to];
}
}
void dfs(int x,int par,int l,int r){
vector <pii> vec;
for (int to: v[x]){
if (to != par) vec.pb({mn[to],to});
}
sort(vec.begin(),vec.end());
int L = l;
for (auto [p,to]: vec){
dfs(to,x,L,L + sub[to] - 1);
L += sub[to];
}
ord[r] = x;
}
void build(int h,int l,int r){
lz[h] = -1;
if (l == r){
t[h] = 0;
return;
}
build(left);
build(right);
t[h] = t[h*2] + t[h*2 + 1];
}
void push(int h,int l,int r){
if (lz[h] == -1) return;
lz[h*2] = lz[h*2+ 1] = lz[h];
t[h*2] = ((r + l)/2 - l + 1)*lz[h];
t[h*2 + 1] = (r - (r + l)/2)*lz[h];
lz[h] = -1;
}
int findk(int h,int l,int r,int k){
if (l == r) return l;
push(h,l,r);
int lft = (l + r)/2 - l + 1 - t[h*2];
if (lft >= k) return findk(left,k);
return findk(right,k - lft);
}
void upd(int h,int l,int r,int L,int R,int vl){
if (r < L || R < l) return;
if (L <= l && r <= R){
t[h] = vl * (r - l + 1);
lz[h] = vl;
return;
}
push(h,l,r);
upd(left,L,R,vl);
upd(right,L,R,vl);
t[h] = t[h*2] + t[h*2 + 1];
}
int get(int h,int l,int r,int idx){
if (l == r) return t[h];
push(h,l,r);
if (idx > (l + r)/2) return get(right,idx);
return get(left,idx);
}
signed main(){
ios_base::sync_with_stdio(0),cin.tie(NULL),cout.tie(NULL);
int n,q,root;
cin>>n>>q;
for (int i = 1; i <= n; i++){
int p;
cin>>p;
if (!p) root=i;
else {
pr[i] = p;
v[p].pb(i);
v[i].pb(p);
}
}
predfs(root,root);
dfs(root,root,1,n);
for (int i = 1; i <= n; i++)
id[ord[i]] = i;
build(1,1,n);
for (int i = 1; i <= 18; i++)
for (int j = 1; j <= n; j++)
d[i][j] = d[i - 1][d[i - 1][j]];
while (q--){
int tp,x;
cin>>tp>>x;
if (tp == 1){
int len = findk(1,1,n,x); // me-x nuli vipovot
upd(1,1,n,1,len,1);
cout<<ord[len]<<endl;
continue;
}
int y = x,len = 0;
for (int i = 18; i >= 0; i--){
if (dep[y] > (1<<i) && get(1,1,n,id[d[i][y]])) {
len += (1<<i);
y = d[i][y];
}
}
upd(1,1,n,id[y],id[y],0);
cout<<len<<endl;
}
}
