#include<bits/stdc++.h>
using namespace std;
const int N = 1e5 + 5, lg = 20;
vector<int> G[N], G2[N];
int n, q, spt[N][lg], h[N], dp[N], s[N], root, a[N];
set<int> S;
map<int, int> mp, mp2;
bool ball[N];
void in() {
cin >> n >> q;
for (int i = 1; i <= n; i++) {
int p;
cin >> p;
a[i] = p;
if (!p)
root = i;
G[i].push_back(p);
G[p].push_back(i);
}
}
void dfs(int u = root, int p = 0) {
spt[u][0] = p;
dp[u] = u;
for (int j = 1; j < lg; j++)
spt[u][j] = spt[spt[u][j - 1]][j - 1];
for (int v : G[u])
if (v != p) {
h[v] = h[u] + 1;
dfs(v, u);
dp[u] = min(dp[u], dp[v]);
}
}
void dfs2(int u = mp2[root], int p = 0) {
spt[u][0] = p;
for (int j = 1; j < lg; j++)
spt[u][j] = spt[spt[u][j - 1]][j - 1];
for (int v : G2[u])
if (v != p) {
h[v] = h[u] + 1;
dfs2(v, u);
}
}
int get_par(int u, int x) {
for (int i = 0; i < lg; i++)
if ((x >> i) & 1)
u = spt[u][i];
return u;
}
int lca(int u, int v) {
if (h[u] < h[v])
swap(u, v);
u = get_par(u, h[u] - h[v]);
if (u == v)
return v;
for (int i = lg - 1; ~i; i--)
if (spt[v][i] != spt[u][i])
u = spt[u][i], v = spt[v][i];
return spt[u][0];
}
bool cmp(const int &a, const int &b) {
int v = a;
int u = b;
int anc = lca(u, v);
if (anc == v)
return false;
if (anc == u)
return true;
v = get_par(v, h[v] - h[anc] - 1);
u = get_par(u, h[u] - h[anc] - 1);
return dp[v] < dp[u];
}
void rem(int k) {
k = mp2[k];
int u = k;
for (int i = lg - 1; ~i; i--)
if (ball[spt[k][i]])
k = spt[k][i];
ball[k] = false;
S.insert(k);
cout << h[u] - h[k] << endl;
}
void add(int k) {
int l;
while(k--) {
l = *S.begin();
ball[l] = true;
S.erase(l);
}
cout << mp[l] << endl;
}
void pre() {
dfs();
for (int i = 1; i <= n; i++)
s[i] = i;
sort(s + 1, s + 1 + n, cmp);
for (int i = 1; i <= n; i++)
mp[i] = s[i], mp2[s[i]] = i;
mp[0] = mp2[0] = 0;
for (int i = 1; i <= n; i++)
S.insert(i);
for (int i = 1; i <= n; i++) {
a[i] = mp2[a[i]];
G2[mp2[i]].push_back(a[i]);
G2[a[i]].push_back(mp2[i]);
h[i] = 0;
}
memset(spt, 0, sizeof spt);
dfs2();
}
void Q() {
while(q--) {
int T, k;
cin >> T >> k;
if(T == 1)
add(k);
else
rem(k);
}
}
int main() {
ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
in();
pre();
Q();
}
