//RESET VALUES OF N TO AVOID RTE :/
#include<bits/stdc++.h>
#define ind(a) scanf("%d", &a)
#define inlld(a) scanf("%lld", &a)
#define pb push_back
#define f first
#define s second
#define ind2(a, b) scanf("%d%d", &a, &b)
#define ind3(a, b, c) scanf("%d%d%d", &a, &b, &c)
#define inlld2(a, b) scanf("%lld%lld", &a, &b)
#define inlld3(a, b, c) scanf("%lld%lld%lld", &a, &b, &c)
using namespace std;
const int N=1e5+5;
const int MOD=1e9+7;
typedef long long ll;
typedef long double ld;
int power(int a,int b,int m = MOD){
if(b == 0) return 1;
if(b == 1) return a;
int x = power(a,b/2,m)%m;
x = (x*x)%m;
if(b%2) return (x*a)%m;
return x;
}
ll n, q, mini[N], lcapar[N][30], order[N], arr[N];
ll height[N];
vector<ll>adj[N];
set<pair<ll, ll> >ss[N];
void dfs1(ll u, ll par, ll h)
{
ll anc=1, i=0;
ll here=1e9;
height[u]=h;
while(anc<=h)
{
if(i==0)
lcapar[u][i]=par;
else
lcapar[u][i]=lcapar[lcapar[u][i-1]][i-1];
anc*=2;
i++;
}
for(auto v:adj[u])
{
if(v==par)
continue;
dfs1(v, u, h+1);
here=min(here, min(mini[v], v));
ss[u].insert({min(mini[v], v), v});
}
mini[u]=here;
}
ll tim=1;
void dfs2(ll u)
{
for(auto v:ss[u])
dfs2(v.s);
order[u]=tim++;
}
set<pair<ll, ll> >finalset;
int main()
{
ll root;
inlld2(n, q);
for(ll a=1; a<=n; a++)
{
ll p;
inlld(p);
if(!p)
root=a;
else
{
adj[a].pb(p);
adj[p].pb(a);
}
}
dfs1(root, 0, 0);
dfs2(root);
for(ll a=1; a<=n; a++)
finalset.insert({order[a], a});
ll ptr=0;
while(q--)
{
ll type, u;
inlld2(type, u);
if(type==1)
{
ll cnt=0, ans;
for(auto it:finalset)
{
cnt++;
arr[it.s]=1;
ans=it.s;
finalset.erase(it);
if(cnt==u)
break;
}
printf("%lld\n", ans);
}
else
{
ll tosub=height[u];
ll i=log2(height[u])+1;
while(i>=0)
{
if(arr[lcapar[u][i]]==1)
{
u=lcapar[u][i];
}
else
i--; //check if correct
}
// printf("%lld ", u);
if(u==0)
printf("%lld\n", tosub+1);
else
printf("%lld\n", tosub-height[u]);
arr[max((ll)1, u)]=0;
finalset.insert({order[u], u});
}
}
return 0;
}
//RESET VALUES OF N TO AVOID RTE :/
