#include <stdio.h>
#include <algorithm>
#include <vector>
#include <functional>
#include <utility>
#define N 100100
#define left(i) (i<<1)
#define right(i) ((i<<1)+1)
#define ii std::pair<int,int>
typedef struct trr{
int sum;
int lz;
}trr;
trr seg[N*4];
void prop(int idx, int l, int r){
if(seg[idx].lz){
if(l != r-1){
int md = (l+r)>>1;
seg[left(idx)].lz = seg[right(idx)].lz = 1;
seg[left(idx)].sum = md-l;
seg[right(idx)].sum = r-md;
seg[idx].sum = seg[left(idx)].sum + seg[right(idx)].sum;
};
seg[idx].lz = 0;
};
};
int up1(int idx, int l, int r, int k){
prop(idx,l,r);
if(l == r-1){
seg[idx].sum = 1;
return l;
}else{
int md = (l+r)>>1;
int r1 = md-l;
int r2 = r-md;
int erg;
if(r1 - seg[left(idx)].sum >= k){
erg = up1(left(idx),l,md,k);
}else{
int tmp = seg[left(idx)].sum;
seg[left(idx)].lz = 1;
seg[left(idx)].sum = r1;
erg = up1(right(idx),md,r,k-r1+tmp);
};
seg[idx].sum = seg[left(idx)].sum + seg[right(idx)].sum;
return erg;
};
};
void up2(int idx, int l, int r, int x){
prop(idx,l,r);
if(l == r-1){
seg[idx].sum = 0;
}else{
int md = (l+r)>>1;
if(x < md){
up2(left(idx),l,md,x);
}else{
up2(right(idx),md,r,x);
};
seg[idx].sum = seg[left(idx)].sum + seg[right(idx)].sum;
};
};
int qry(int idx, int l, int r, int x){
prop(idx,l,r);
if(l == r-1){
return seg[idx].sum;
}else{
int md = (l+r)>>1;
if(x < md){
return qry(left(idx),l,md,x);
}else{
return qry(right(idx),md,r,x);
};
};
};
int in[N];
int mp[N];
int cnt = 0;
int par[N][20];
int ptz[20];
int mn[N];
std::vector<ii> adj[N];
void dfs1(int v, int p){
mn[v] = v;
for(int i = 0;i<adj[v].size();i++){
ii akt = adj[v][i];
dfs1(akt.second,v);
mn[v] = std::min(mn[v],mn[akt.second]);
adj[v][i].first = mn[akt.second];
};
};
void dfs(int v, int p){
par[v][0] = p;
for(int i = 1;i<20;i++){
par[v][i] = par[par[v][i-1]][i-1];
};
for(auto i: adj[v]){
if(!in[i.second]){
dfs(i.second,v);
};
};
in[v] = cnt++;
mp[in[v]] = v;
};
int n;
int ib(int idx){
if(idx == 0)return 0;
else return qry(1,0,n,in[idx]);
};
int main(void){
ptz[0] = 1;
for(int i = 1;i<20;i++){
ptz[i] = ptz[i-1] * 2;
};
int q;
scanf("%d %d",&n,&q);
int pp;
int rr;
for(int i = 1;i<=n;i++){
scanf("%d",&pp);
if(pp){
adj[pp].push_back({0,i});
}else{
rr = i;
};
};
dfs1(rr,0);
for(int i = 1;i<=n;i++){
std::sort(adj[i].begin(),adj[i].end(),std::less<ii>());
};
dfs(rr,0);
int k;
for(int i = 0;i<q;i++){
scanf("%d %d",&k,&pp);
if(k == 1){
printf("%d\n",mp[up1(1,0,n,pp)]);
}else{
int akt = pp;
int erg = 0;
for(int i = 19;i>=0;i--){
if(ib(par[akt][i])){
erg += ptz[i];
akt = par[akt][i];
};
};
up2(1,0,n,in[akt]);
printf("%d\n",erg);
};
};
return 0;
};
