#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 1e5 + 10;
vector<int> t[maxn];
int mnm[maxn], ft[maxn], pos[maxn], Time = 1;
int par[maxn][20];
int seg[4*maxn], lazy[4*maxn];
void shift(int,int,int);
int get(int id, int L, int R, int l, int r){
if (r <= L or R <= l)
return 0;
if (l <= L and R <= r)
return seg[id];
shift(id,L,R);
int mid = (L + R) >> 1;
return get(2*id+0, L, mid, l, r) + get(2*id+1, mid, R, l, r);
}
void change(int id, int L, int R, int l, int r, int val){
if (r <= L or R <= l)
return;
if (l <= L and R <= r){
seg[id] = (R-L) * val;
lazy[id] = val;
return;
}
int mid = (L + R) >> 1;
shift(id,L,R);
change(2*id+0, L, mid, l, r, val);
change(2*id+1, mid, R, l, r, val);
seg[id] = seg[2*id+0] + seg[2*id+1];
}
void shift(int id, int L, int R){
if (lazy[id] == -1)
return;
int mid = (L + R) >> 1;
change(2*id+0, L, mid, L, mid, lazy[id]);
change(2*id+1, mid, R, mid, R, lazy[id]);
lazy[id] = -1;
}
void dfs(int v){
for (auto u : t[v])
dfs(u);
ft[v] = Time;
pos[Time++] = v;
}
int dfsinit(int v){
mnm[v] = v;
for (auto u : t[v])
mnm[v] = min(mnm[v], dfsinit(u));
sort(t[v].begin(), t[v].end(), [](int x, int y){ return mnm[x] < mnm[y]; });
return mnm[v];
}
int main(){
ios_base::sync_with_stdio(false);
int n, q;
cin >> n >> q;
int root = -1;
memset(par, -1, sizeof par);
for (int i = 1; i <= n; i++){
int p;
cin >> p;
if (p == 0)
root = i;
else{
t[p].push_back(i);
par[i][0] = p;
}
}
for (int i = 1; i <= 17; i++)
for (int v = 1; v <= n; v++)
if (par[v][i-1] != -1)
par[v][i] = par[par[v][i-1]][i-1];
dfsinit(root);
dfs(root);
memset(lazy, -1, sizeof lazy);
while (q --){
int type, x;
cin >> type >> x;
if (type == 1){
int lo = 0, hi = n+1;
while (hi - lo > 1){
int mid = (lo + hi) >> 1;
if (mid - get(1,1,n+1,1,mid+1) >= x)
hi = mid;
else
lo = mid;
}
change(1,1,n+1,1,hi+1,1);
cout << pos[hi] << '\n';
}
else{
int ans = 0;
for (int i = 17; i >= 0; i--)
if (par[x][i] != -1 and get(1,1,n+1,ft[par[x][i]],ft[par[x][i]]+1) == 1)
x = par[x][i], ans += (1 << i);
cout << ans << '\n';
change(1,1,n+1,ft[x],ft[x]+1,0);
}
}
}
