#include <iostream>
#include <cstdio>
#include <algorithm>
#include <string.h>
#include <vector>
using namespace std;
#define endl '\n'
#define ll long long
#define pi pair<int, int>
#define f first
#define s second
const int mxn = 100001, k = __lg(mxn) + 1;
struct BIT{
int bit[mxn];
BIT(){
memset(bit, 0, sizeof(bit));
}
void add(int x, int v){
for(x++; x < mxn; x += x & -x) bit[x] += v;
}
int qry(){
int ret = 0, s = 0;
for(int i = k - 1; ~i; i--){
ret |= 1 << i;
if(ret >= mxn || bit[ret] + s < ret) ret ^= 1 << i;
else s += bit[ret];
}
return ret;
}
};
int n, q;
int mn[mxn], id[mxn], rid[mxn], vis[mxn];
int p[k][mxn];
vector<int> g[mxn];
BIT bit;
int rt, tt;
int dfs(int c){
mn[c] = c;
for(int i = 1; i < k; i++) p[i][c] = ~p[i - 1][c] ? p[i - 1][p[i - 1][c]] : -1;
for(int i : g[c]) mn[c] = min(mn[c], dfs(i));
return mn[c];
}
void dfs2(int c){
sort(g[c].begin(), g[c].end(), [&](int x, int y){
return mn[x] < mn[y];
});
for(int i : g[c]) dfs2(i);
rid[id[c] = tt++] = c;
}
int main(){
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n >> q;
for(int i = 0; i < n; i++){
cin >> p[0][i];
g[--p[0][i]].push_back(i);
if(!~p[0][i]) rt = i;
}
dfs(rt);
dfs2(rt);
while(q--){
int t, x;
cin >> t >> x;
if(!~-t){
int c = -1;
while(x--){
c = bit.qry();
vis[rid[c]] = 1;
bit.add(c, 1);
}
cout << rid[c] + 1 << endl;
}else{
x--;
int ret = 0;
for(int i = k - 1; ~i; i--){
if(~p[i][x] && vis[p[i][x]]){
ret |= 1 << i;
x = p[i][x];
}
}
vis[x] = 0;
bit.add(id[x], -1);
cout << ret << endl;
}
}
return 0;
}
