#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<vector>
#include<queue>
#include<bitset>
#include<string>
#include<stack>
#include<set>
#include<unordered_set>
#include<map>
#include<unordered_map>
#include<cstring>
#include<complex>
#include<cmath>
#include<iomanip>
#include<numeric>
#include<algorithm>
#include<list>
#include<functional>
#include<cassert>
#define mp make_pair
#define pb push_back
#define X first
#define Y second
#define y0 y12
#define y1 y22
#define INF 987654321987654321
#define PI 3.141592653589793238462643383279502884
#define fup(i,a,b,c) for(int (i)=(a);(i)<=(b);(i)+=(c))
#define fdn(i,a,b,c) for(int (i)=(a);(i)>=(b);(i)-=(c))
#define MEM0(a) memset((a),0,sizeof(a));
#define MEM_1(a) memset((a),-1,sizeof(a));
#define ALL(a) a.begin(),a.end()
#define SYNC ios_base::sync_with_stdio(false);cin.tie(0)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int, int> Pi;
typedef pair<ll, ll> Pll;
typedef pair<ld, ld> Pd;
typedef vector<int> Vi;
typedef vector<ll> Vll;
typedef vector<double> Vd;
typedef vector<Pi> VPi;
typedef vector<Pll> VPll;
typedef vector<Pd> VPd;
typedef tuple<int, int, int> iii;
typedef tuple<int,int,int,int> iiii;
typedef tuple<ll, ll, ll> LLL;
typedef vector<iii> Viii;
typedef vector<LLL> VLLL;
typedef complex<double> base;
const ll MOD = 1000000007;
ll POW(ll a, ll b, ll MMM = MOD) {ll ret=1; for(;b;b>>=1,a=(a*a)%MMM)if(b&1)ret=(ret*a)% MMM; return ret; }
ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; }
ll lcm(ll a, ll b) { if (a == 0 || b == 0)return a + b; return a*(b / gcd(a, b)); }
int dx[] = { 0,1,0,-1,1,1,-1,-1 }, dy[] = { 1,0,-1,0,1,-1,1,-1 };
int n,q,R;
Vi v[100001];
int mn[100001],parent[100001][17];
void dfs1(int N)
{
mn[N]=N;
for(int next:v[N])
{
parent[next][0]=N;
dfs1(next);
mn[N]=min(mn[N],mn[next]);
}
sort(ALL(v[N]),[&](int a,int b){
return mn[a]<mn[b];
});
}
Vi vv,rv;
bool chk[100001];
void dfs2(int N)
{
for(int next:v[N])
{
dfs2(next);
}
vv.pb(N);
}
int tree[262144];
void upd(int node, int S, int E, int k, int dif)
{
tree[node] += dif;
if (S == E)return;
if (k <= (S + E) / 2)upd(node * 2, S, (S + E) / 2, k, dif);
else upd(node * 2 + 1, (S + E) / 2 + 1, E, k, dif);
}
int find(int node, int S, int E)
{
if(S==E)return S;
int M=(S+E)>>1;
if(tree[node*2]!=M-S+1)return find(node*2,S,M);
else return find(node*2+1,M+1,E);
}
int go(){
int t=find(1,0,n-1);
upd(1,0,n-1,t,1);
chk[vv[t]]=1;
return vv[t];
}
int main() {
MEM_1(parent);
scanf("%d%d",&n,&q);
fup(i,0,n-1,1)
{
int x;
scanf("%d",&x);
if(x)v[x-1].pb(i);
else R=i;
}
dfs1(R);dfs2(R);
fup(j,0,15,1)
fup(i,0,n-1,1)
{
if(parent[i][j]!=-1)
{
parent[i][j+1]=parent[parent[i][j]][j];
}
}
rv.resize(n);
fup(i,0,n-1,1)rv[vv[i]]=i;
while(q--)
{
int o,x;
scanf("%d%d",&o,&x);
if(o==1)
{
int ans=-1;
while(x--)ans=go();
printf("%d\n",ans+1);
}
else
{
int ans=0;
int now=x-1;
fdn(i,16,0,1)
{
if(parent[now][i]!=-1 && chk[parent[now][i]])
{
now=parent[now][i];
ans+=(1<<i);
}
}
chk[now]=0;
upd(1,0,n-1,rv[now],-1);
printf("%d\n",ans);
}
}
}
