#include<bits/stdc++.h>
using namespace std;
struct lazy {
int sz;
vector<int> st, lz;
lazy(vector<int>& ord) {
sz=ord.size();
while (sz&(sz-1)) sz++;
st.assign(2*sz, 0);
for (int i = sz; i < sz+ord.size(); i++) st[i]=1;
for (int i = sz-1; i > 0; i--) st[i]=st[2*i]+st[2*i+1];
lz.assign(2*sz, 0);
}
int find(int x, int n=1, int nl=1, int nr=1) {
if (n==1) nr=sz;
push(n, nl, nr);
if (nl==nr) return nl;
if (st[2*n]>=x) return find(x, 2*n, nl, (nl+nr)/2);
else return find(x-st[2*n], 2*n+1, (nl+nr)/2+1, nr);
}
void push(int n, int l, int r) {
if (lz[n]==0) return;
if (l<r) lz[2*n]=lz[2*n+1]=1;
st[n]=lz[n]=0;
}
void set(int l, int r, int v, int n=1, int nl=1, int nr=1) {
if (n==1) nr=sz;
push(n, nl, nr);
if (nr<l || r<nl) return;
if (l<=nl && nr<=r) {
if (v==0) { lz[n]=1; push(n, nl, nr); return; }
else { st[n]=1; return; }
}
set(l, r, v, 2*n, nl, (nl+nr)/2);
set(l, r, v, 2*n+1, (nl+nr)/2+1, nr);
st[n]=st[2*n]+st[2*n+1];
}
int get(int p, int n=1, int nl=1, int nr=1) {
if (n==1) nr=sz;
push(n, nl, nr);
if (nl==nr) return st[n];
else if (p<=(nl+nr)/2) return get(p, 2*n, nl, (nl+nr)/2);
else return get(p, 2*n+1, (nl+nr)/2+1, nr);
}
};
const int inf=1e9;
vector<int> dp;
vector<vector<int>> cld;
bool comp(int u, int v) { return dp[u]<dp[v]; }
void dfs(int u) {
dp[u]=min(dp[u], u);
for (auto v : cld[u]) {
dfs(v);
dp[u]=min(dp[v], dp[u]);
} sort(cld[u].begin(), cld[u].end(), comp);
}
vector<int> tin, tout, ord;
void eul(int u) {
tin[u]=ord.size()+1;
for (auto v : cld[u]) eul(v);
ord.push_back(u);
tout[u]=ord.size();
}
int main() {
cin.tie(0)->sync_with_stdio(false);
int n, q, r;
cin >> n >> q;
vector<int> par(n+1, 0);
cld.assign(n+1, vector<int>());
for (int i = 1; i <= n; i++) {
cin >> par[i];
cld[par[i]].push_back(i);
if (par[i]==0) r=i;
}
dp.assign(n+1, inf);
for (int i = 1; i <= n; i++) dp[i]=i;
dfs(r);
tin.assign(n+1, 0);
tout.assign(n+1, 0);
eul(r);
lazy st(ord);
int lg=0;
while (n>=(1<<lg)) lg++;
vector<vector<int>> bl(n+1, vector<int>(lg+1, 0));
for (int i = 1; i <= n; i++) bl[i][0]=par[i];
for (int i = 1; i <= lg; i++) {
for (int j = 1; j <= n; j++) {
bl[j][i]=bl[bl[j][i-1]][i-1];
}
}
while (q--) {
int t, x;
cin >> t >> x;
if (t==1) {
int r=st.find(x);
st.set(1, r, 0);
cout << ord[r-1] << '\n';
} else {
int r=x, a=0;
for (int i = lg; i >= 0; i--) {
if (bl[r][i]==0 || st.get(tout[bl[r][i]])==1) continue;
a+=1<<i; r=bl[r][i];
} st.set(tout[r], tout[r], 1);
cout << a << '\n';
}
}
return 0;
}
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