#include <bits/stdc++.h>
#define FOR(x, a, b) for (int x = a; x <= b; ++x)
#define FOD(x, a, b) for (int x = a; x >= b; --x)
#define REP(x, a, b) for (int x = a; x < b; ++x)
#define DEBUG(X) { cout << #X << " = " << X << endl; }
#define PR(A, n) { cout << #A << " = "; FOR(_, 1, n) cout << A[_] << " "; cout << endl; }
#define PR0(A, n) { cout << #A << " = "; REP(_, 0, n) cout << A[_] << " "; cout << endl; }
using namespace std;
typedef long long LL;
typedef pair <int, int> II;
const int N = 1e5 + 10;
int n, q, Root, timer = 0, eulerSize = 0;
int x[N], V[N], c[N], pos[N], euler[N];
int headChain[N], szChain[N], p[N];
vector <int> adj[N];
set <II> S;
struct SegmentTree {
#define m ((l + r) >> 1)
int st[4 * N];
void Build(int k, int l, int r) {
st[k] = 0;
if (l == r) return;
Build(k << 1, l, m);
Build(k << 1 | 1, m + 1, r);
}
void Update(int k, int l, int r, int i, int v) {
if (l == r) {
st[k] += v;
return;
}
if (i <= m) Update(k << 1, l, m, i, v);
else Update(k << 1 | 1, m + 1, r, i, v);
st[k] = st[k << 1] + st[k << 1 | 1];
}
int Query(int k, int l, int r, int i, int j) {
if (l > j || r < i) return 0;
if (i <= l && r <= j) return st[k];
return Query(k << 1, l, m, i, j) + Query(k << 1 | 1, m + 1, r, i, j);
}
#undef m
} ST;
void EulerTour(int u) {
REP(k, 0, adj[u].size()) {
int v = adj[u][k];
EulerTour(v);
}
euler[++eulerSize] = u;
}
void DFS(int u) {
c[u] = 1;
REP(k, 0, adj[u].size()) {
int v = adj[u][k];
DFS(v);
c[u] += c[v];
}
}
void HLD(int u, int par) {
szChain[par]++;
headChain[u] = par;
x[u] = ++timer; V[timer] = u;
int vtx = 0;
REP(k, 0, adj[u].size()) {
int v = adj[u][k];
if (vtx == 0 || c[v] > c[vtx]) vtx = v;
}
if (vtx != 0) HLD(vtx, par);
REP(k, 0, adj[u].size()) {
int v = adj[u][k]; if (v == vtx) continue;
HLD(v, v);
}
}
int Insert(int num) {
for (set <II> :: iterator it = S.begin(); it != S.end(); ++it) {
--num;
int u = it -> second;
ST.Update(1, 1, n, x[u], +1);
if (num == 0) return u;
}
assert(false);
}
void Add(int i, int v) {
ST.Update(1, 1, n, i, v);
S.insert(II(pos[V[i]], V[i]));
}
int Remove(int u, int a = Root) {
int uChain = headChain[u], aChain = headChain[a];
int nxt = -1, ans = 0;
bool flag = false;
while (true) {
if (uChain == aChain) {
int k = ST.Query(1, 1, n, x[a], x[u]);
int i = x[u] - k + 1;
Add(i, -1);
ans += k;
flag = true;
return ans;
}
int l = x[uChain], r = x[u];
int k = ST.Query(1, 1, n, l, r);
ans += k;
if (r - l + 1 == k) {
nxt = x[uChain];
} else if (r - l + 1 != 0) {
int i = x[u] - k + 1;
Add(i, -1);
flag = true;
return ans;
} else {
Add(nxt, -1);
flag = true;
return ans;
}
u = p[uChain]; uChain = headChain[u];
}
if (flag == false) Add(nxt, -1);
return ans;
}
int main() {
#ifdef LOCAL
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif // LOCAL
scanf("%d%d", &n, &q);
FOR(i, 1, n) {
scanf("%d", &p[i]);
if (p[i] == 0) Root = i;
else adj[p[i]].push_back(i);
}
FOR(i, 1, n) sort(adj[i].begin(), adj[i].end());
DFS(Root);
HLD(Root, Root);
EulerTour(Root);
FOR(i, 1, eulerSize) pos[euler[i]] = i;
FOR(i, 1, n) S.insert(II(pos[i], i));
ST.Build(1, 1, n);
FOR(timer, 1, q) {
int t, u; scanf("%d%d", &t, &u);
if (t == 1) printf("%d\n", Insert(u));
else printf("%d\n", Remove(u) - 1);
}
return 0;
}
