#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int> ii;
const int N = 1e5+10;
int n, q, p[N][18], root, sub[N], lev[N], idx[N];
vector<int> g[N];
deque<int> eul;
int dfs(int u, int f, int l) {
sub[u] = u;
lev[u] = l;
for(int v : g[u]) if(v != f)
sub[u] = min(sub[u], dfs(v,u,l+1));
return sub[u];
}
void flat(int u, int f) {
vector<ii> tmp;
for(int v : g[u]) if(v != f)
tmp.push_back({sub[v],v});
sort(tmp.begin(),tmp.end());
for(auto v : tmp)
flat(v.second,u);
eul.push_back(u);
}
struct segtree {
int t[N<<2], stat[N];
void build(int node, int L, int R) {
if(L == R) return void(t[node] = stat[L] = 1);
int mid = (L+R)>>1, lc = node<<1, rc = lc|1;
build(lc,L,mid), build(rc,mid+1,R);
t[node] = t[lc] + t[rc];
}
bool check(int pos) { return stat[pos]; }
void on(int node, int L, int R, int pos) {
if(L == R) return void(t[node] = stat[L] = 1);
int mid = (L+R)>>1, lc = node<<1, rc = lc|1;
pos <= mid ? on(lc,L,mid,pos) : on(rc,mid+1,R,pos);
t[node] = t[lc] + t[rc];
}
void off(int node, int L, int R, int pos) {
if(L == R) return void(t[node] = stat[L] = 0);
int mid = (L+R)>>1, lc = node<<1, rc = lc|1;
pos <= mid ? off(lc,L,mid,pos) : off(rc,mid+1,R,pos);
t[node] = t[lc] + t[rc];
}
int kth(int node, int L, int R, int k) {
if(L == R) return L;
int mid = (L+R)>>1, lc = node<<1, rc = lc|1;
if(k <= t[lc]) return kth(lc,L,mid,k);
return kth(rc,mid+1,R,k-t[lc]);
}
}ds;
int main() {
memset(p,-1,sizeof p);
scanf("%d %d", &n, &q);
for(int i = 1; i <= n; i++) {
int v;
scanf("%d", &v);
if(v) g[i].push_back(v), g[v].push_back(i), p[i][0] = v;
if(!v) root = i;
}
for(int j = 1; j < 18; j++)
for(int i = 1; i <= n; i++)
if(p[i][j-1] != -1)
p[i][j] = p[p[i][j-1]][j-1];
dfs(root,-1,0);
flat(root,-1);
/*for(int i = 0; i < n; i++)
cout << eul[i] << " ";
cout << endl;*/
for(int i = 0; i < n; i++)
idx[eul[i]] = i;
ds.build(1,0,n-1);
while(q--) {
int t, x;
scanf("%d %d", &t, &x);
if(t == 1) {
int idx;
while(x--) {
idx = ds.kth(1,0,n-1,1);
//cout << "goes to " << eul[idx] << endl;
ds.off(1,0,n-1,idx);
}
printf("%d\n", eul[idx]);
}
else {
int u = x;
for(int i = 17; i >= 0; i--) {
if(p[u][i] != -1 && ds.check(idx[p[u][i]]) == 0)
u = p[u][i];
}
//cout << "biggest on parent = " << u << endl;
ds.on(1,0,n-1,idx[u]);
printf("%d\n", lev[x] - lev[u]);
}
//for(int i = 0; i < n; i++)
//cout << eul[i] << " " << ds.check(i-1) << endl;
}
return 0;
}
