#include <bits/stdc++.h>
using namespace std;
const int MAXN = 100010;
const int LOGN = 20;
struct node{
int sum, lz;
node(){
sum = 0;
lz = -1;
}
};
int t = 0;
int tin[MAXN], tout[MAXN], submin[MAXN], posicao[MAXN], pai[MAXN], dist[MAXN];
node seg[4 * MAXN];
int up[LOGN+10][MAXN];
vector<int> grafo[MAXN];
bool cmp(int i, int j){
return submin[i] < submin[j];
}
void dfs(int v, int p, int id){
submin[v] = v;
for(auto viz : grafo[v]){
if(viz == p) continue;
dist[viz] = dist[v] + 1;
dfs(viz, v, id);
submin[v] = min(submin[v], submin[viz]);
}
if(id == 1){
tout[v] = ++t;
posicao[t] = v;
return;
}
for(int i = 0; i < grafo[v].size(); i++){
sort(grafo[v].begin(), grafo[v].end(), cmp);
}
return;
}
void refresh(int pos, int ini, int fim){
if(seg[pos].lz == -1){
//printf("deu em %d\n", pos);
return;
}
if(ini == fim){
seg[pos].sum = seg[pos].lz;
seg[pos].lz = -1;
return;
}
int e = 2 * pos, d = 2 * pos + 1;
seg[e].lz = seg[pos].lz;
seg[d].lz = seg[pos].lz;
seg[pos].sum = (fim - ini + 1) * seg[pos].lz;
seg[pos].lz = -1;
return;
}
void update(int pos, int ini, int fim, int l, int r, int val){
refresh(pos, ini, fim);
if(ini > r || fim < l) return;
if(l <= ini && fim <= r){
seg[pos].lz = val;
refresh(pos, ini, fim);
return;
}
int m = (ini + fim) / 2;
int e = 2 * pos, d = 2 * pos + 1;
update(e, ini, m, l, r, val);
update(d, m + 1, fim, l, r, val);
seg[pos].sum = seg[e].sum + seg[d].sum;
return;
}
int bsseg(int pos, int ini, int fim, int s){
if(ini == fim){
return ini;
}
//refresh(pos, ini, fim);
int m = (ini + fim) / 2;
int e = 2 * pos, d = 2 * pos + 1;
refresh(e, ini, m), refresh(d, m + 1, fim);
if(seg[e].sum >= s) return bsseg(e, ini, m, s);
return bsseg(d, m + 1, fim, s - seg[e].sum);
}
int query(int pos, int ini, int fim, int id){
if(id < ini || id > fim) return 0;
if(seg[pos].lz != -1){
int resp = seg[pos].lz;
refresh(pos, ini, fim);
return resp;
}
refresh(pos, ini, fim);
if(ini == fim) return seg[pos].sum;
int m = (ini + fim) / 2;
int e = 2 * pos, d = 2 * pos + 1;
if(id <= m) return query(e, ini, m, id);
return query(d, m + 1, fim, id);
}
void calcup(int n){
for(int i = 1; i <= n; i++){
up[0][i] = pai[i];
}
for(int k = 1; k < LOGN; k++){
for(int i = 1; i <= n; i++){
up[k][i] = up[k - 1][ up[k - 1][i] ];
}
}
return;
}
int bsbl(int v, int n){
for(int k = LOGN - 1; k >= 0; k--){
int l = tout[ up[k][v] ];
if(!query(1, 1, n, l)){
//printf("deu no k = %d\n", k);
v = up[k][v];
}
}
return v;
}
template<typename T> void read(T& aa)
{
aa=0;
char cc=getchar();
T ff=1;
while((cc != '-') && (cc < '0' || cc > '9')) cc=getchar();
if(cc=='-') ff=-1, cc=getchar();
while(cc >= '0' && cc <= '9') aa = aa*10 + cc - '0', cc=getchar();
aa*=ff;
}
int main(){
cin.tie(0)->sync_with_stdio(0);
int n, q; read(n), read(q);
int root;
update(1, 1, n, 1, n, 1);
for(int i = 1; i <= n; i++){
int v; read(v);
if(v == 0){
root = i;
pai[root] = root;
continue;
}
pai[i] = v;
grafo[i].push_back(v);
grafo[v].push_back(i);
}
dfs(root, root, 0);
dfs(root, root, 1);
calcup(n);
for(int i = 1; i <= q; i++){
int type; read(type);
if(type == 1){
int k; read(k);
int t = bsseg(1, 1, n, k);
cout << posicao[t] << '\n';
update(1, 1, n, 1, t, 0);
}
if(type == 2){
int x; read(x);
int r = bsbl(x, n);
cout << dist[x] - dist[r] << '\n';
update(1, 1, n, tout[r], tout[r], 1);
}
}
/*for(int i = 1; i <= n; i++){
printf("up[%d]:\n", i);
for(int k = 0; k < LOGN; k++){
printf("\tup[%d][%d] = %d\n", k, i, up[k][i]);
}
}*/
/*for(int i = 1; i <= q; i++){
int type; scanf("%d", &type);
if(type == 1){
int l, r, val; scanf("%d %d %d", &l, &r, &val);
update(1, 1, n, l, r, val);
}
if(type == 2){
int s; scanf("%d", &s);
printf("%d\n", bs(1, 1, n, s));
}
}*/
return 0;
}
