#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mp make_pair
#define pb push_back
#define x first
#define y second
#define pii pair<int, int>
#define p3i pair<pii, int>
#define pll pair<ll, ll>
#define p3l pair<pll, ll>
#define lseg L, (L+R)/2, N*2+1
#define rseg (L+R)/2+1, R, N*2+2
#define ub upper_bound
#define lb lower_bound
#define pq priority_queue
#define MN 1000000007
#define fox(k, x) for (int k=0; k<x; ++k)
#define fox1(k, x) for (int k=1; k<=x; ++k)
#define foxr(k, x) for (int k=x-1; k>=0; --k)
#define fox1r(k, x) for (int k=x; k>0; --k)
#define ms multiset
#define flood(x) memset(x, 0x3f3f3f3f, sizeof x)
#define drain(x) memset(x, 0, sizeof x)
int n, m, r, p, t, x, c=0;
int a[100005], o[100005], d[100005], sub[100005], sp[20][100005];
bool u[100005];
vector<int> v[100005];
set<pii> s;
void dfs(int N, int P){
sub[N]=N;
sp[0][N]=P;
if (P==-1) d[P]=0;
else d[N]=d[P]+1;
fox1(l, 18){
if (sp[l-1][N]==-1) sp[l][N]=-1;
else sp[l][N]=sp[l-1][sp[l-1][N]];
}
//cout << N << ": \n";
//fox(l, 4) cout << sp[l][N] << ' '; cout << endl;
fox(l, v[N].size()){
dfs(v[N][l], N);
sub[N]=min(sub[N], sub[v[N][l]]);
}
}
void dfs2(int N){
vector<pii> ord;
fox(l, v[N].size()){
ord.pb(mp(sub[v[N][l]], v[N][l]));
}
sort(ord.begin(), ord.end());
fox(l, ord.size()){
dfs2(ord[l].y);
}
o[N]=++c;
s.insert(mp(o[N], N));
}
int an(int X){
int k=18;
while(k>0){
while(k>0 && (sp[k][X]==-1 || !u[sp[k][X]])){
k--;
}
if (sp[k][X]==-1 || !u[sp[k][X]]) break;
X=sp[k][X];
}
s.insert(mp(o[X], X));
u[X]=0;
//cout << X << ' ' << d[X] << endl;
return d[X];
}
int main(){
scanf("%i%i", &n, &m);
fox1(l, n){
scanf("%i", &p);
v[p].pb(l);
}
dfs(0, -1);
dfs2(0);
c=0;
fox(l, m){
scanf("%i%i", &t, &x);
if (t==1){
fox(l2, x){
u[s.begin()->y]=1;
t=s.begin()->y;
s.erase(s.begin());
}
printf("%i\n", t);
} else {
//cout << x << ' ';
printf("%i\n", d[x]-an(x));
}
}
return 0;
}
