#include <bits/stdc++.h>
#define all(x) x.begin(), x.end()
#define fi(i, a, b) for(int i = a; i <= b; i++)
#define fid(i, a, b) for(int i = a; i >= b; i--)
#define maxn (int) 2e5 + 7
using namespace std;
int n, q, N;
int cl[maxn], vt[maxn], cha[maxn][18];
int Min[maxn], a[maxn];
vector<int> edges[maxn];
set<int> S;
void pre_dfs(int u, int par) {
for(int v : edges[u]) if(v != par) {
pre_dfs(v, u);
Min[u] = min(Min[u], Min[v]);
}
}
int In[maxn], Out[maxn], Time;
void dfs(int u, int par) {
for(int v : edges[u]) if(v != par) {
cha[v][0] = u; fi(i, 1, 17) cha[v][i] = cha[cha[v][i - 1]][i - 1];
dfs(v, u);
}
a[++N] = u, vt[u] = N;
}
int Add(int k, int ans = 0) {
while(k--) {
ans = a[*S.begin()];
cl[a[*S.begin()]] = 1, S.erase(S.begin());
}
return ans;
}
int Del(int u, int ans = 0) {
fid(i, 17, 0) if(cl[cha[u][i]]) u = cha[u][i], ans += (1 << i);
S.insert(vt[u]), cl[u] = 0;
return ans;
}
int main()
{
cin >> n >> q;
int rt = 0;
fi(i, 1, n) {
Min[i] = i, S.insert(i);
int x; cin >> x;
if(x == 0) rt = i;
else edges[x].push_back(i);
}
pre_dfs(rt, 0);
fi(i, 1, n) sort(all(edges[i]), [](int x, int y) { return Min[x] < Min[y]; } );
dfs(rt, 0);
fi(i, 1, q) {
int type, x; cin >> type >> x;
if(type == 1) cout << Add(x) << '\n';
else cout << Del(x) << '\n';
}
return 0;
}
