#include <bits/stdc++.h>
using namespace std;
#define fastIO ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
#define FF first
#define SS second
#define pb push_back
#define sz(x) (int)x.size()
#define oo 1e9
#define PI acos(-1.0)
#define lb lower_bound
#define ub upper_bound
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> ii;
const int N = 1e5+7, M=18;
const int MOD = 1e9+7;
int n, m, k, t;
int P[N][M], fen[N], h[N];
vector<int> adj[N];
int pos[N], idx[N];
int _dp[N], cnt=0;
bool cmp(const int &a, const int &b) {return _dp[a]<_dp[b];}
void dfs(int u) {
_dp[u]=u;
for(int v, i=0;i<sz(adj[u]);i++) {
v=adj[u][i], h[v]=h[u]+1, P[v][0]=u;
dfs(v), _dp[u]=min(_dp[u], _dp[v]);
}
}
void dfs2(int u) {
for(int i=0;i<sz(adj[u]);i++) dfs2(adj[u][i]);
pos[u]=++cnt, idx[cnt]=u;
}
void process(int s) {
h[s]=-1, dfs(s);
for(int i=1;i<=n;i++) sort(adj[i].begin(), adj[i].end(), cmp);
dfs2(s);
for(int j=1;(1<<j)<=n;j++) for(int i=1;i<=n;i++)
P[i][j]=P[P[i][j-1]][j-1];
}
void upd(int i, int v) {for(;i<=n;i+=i&-i) fen[i]+=v;}
int get(int i) {int res=0;for(;i>0;i-=i&-i) res+=fen[i];return res;}
signed main() {
//freopen("test.inp", "r", stdin);
//freopen("test.out", "w", stdout);
//fastIO;
scanf("%d%d", &n, &m);int u;
for(int i=1;i<=n;adj[u].pb(i++)) scanf("%d", &u);
process(0);
for(int ans=0, i=1;i<=m;ans=0, i++) {
scanf("%d%d", &t, &k);
if(t&1) {
for(int j=1;j<=k;j++) {
int l=1, mid, r=n;ans=n;
while(l<=r) {
mid=(l+r)/2;
if(get(mid)==mid) l=mid+1;
else ans=mid, r=mid-1;
}
upd(ans, 1), ans=idx[ans];
}
} else {
for(int tmp, i=log2(h[k]);i>=0;i--) {
tmp=get(pos[P[k][i]])-get(pos[P[k][i]]-1);
if(tmp) k=P[k][i], ans+=(1<<i);
}
upd(pos[k], -1);
}
printf("%d\n", ans);
}
return 0;
}
/* stuff you should look for
- int overflow, array bounds
- special cases (n=1?)
- do smth instead of do nothing and stay organized
- WRITE STUFF DOWN
- DONT JUST STICK ON ONE APPROACH
*/
