#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define sz(s) (int)s.size()
#define bit(i, j) ((j >> i) & 1)
#define all(v) v.begin(), v.end()
#define taskname "file"
typedef long long ll;
const int N = 1e5;
int n, q, idx = 0, in[N + 5], ou[N + 5], p[N + 5], lz[4 * N + 5], pa[N + 5][20], depth[N + 5], st[20][N + 5], pp[N + 5];
vector <int> order, g[N + 5];
struct node{
int cnt0, cnt1;
} sg[4 * N + 5];
void dfs(int i){
for(int j : g[i]){
pa[j][0] = i;
depth[j] = depth[i] + 1;
for (int k = 1; k < 20; ++k)
pa[j][k] = pa[pa[j][k - 1]][k - 1];
dfs(j);
in[i] = (!in[i] ? in[j] : min(in[i], in[j]));
}
order.push_back(i);
ou[i] = ++idx;
pp[idx] = i;
if (!in[i]) in[i] = idx;
}
void build1(){
for (int i = 1; i <= n; ++i) st[0][i] = ou[order[i - 1]];
for (int i = 1; i < 20; ++i)
for (int j = 1; j <= n - (1 << i) + 1; ++j)
st[i][j] = max(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
}
int getmin(int l, int r){
int b = __lg(r - l + 1);
return pp[max(st[b][l], st[b][r - (1 << b) + 1])];
}
int parent(int i, int p){
for (int k = 19; k >= 0; --k)
if (p >= (1 << k)){
p -= (1 << k);
i = pa[i][k];
}
return i;
}
node mer(node a, node b){
a.cnt0 += b.cnt0;
a.cnt1 += b.cnt1;
return a;
}
void build(int id, int l, int r){
lz[id] = -1;
sg[id] = {r - l + 1, 0};
if (l == r) return;
int md = (l + r) >> 1;
build(id << 1, l, md);
build(id << 1 | 1, md + 1, r);
}
void pus(int id, int l, int r){
if (lz[id] == -1) return;
if (l != r){
lz[id << 1] = lz[id << 1 | 1] = lz[id];
}
if (lz[id]) sg[id] = {0, r - l + 1};
else sg[id] = {r - l + 1, 0};
lz[id] = -1;
}
void update(int id, int l, int r, int x, int y, int val){
pus(id, l, r);
if (l > y || r < x) return;
if (l >= x && r <= y){
lz[id] = val;
pus(id, l, r);
return;
}
int md = (l + r) >> 1;
update(id << 1, l, md, x, y, val);
update(id << 1 | 1, md + 1, r, x, y, val);
sg[id] = mer(sg[id << 1], sg[id << 1 | 1]);
}
int get(int id, int l, int r, int pos){
pus(id, l, r);
if (l > pos || r < pos) return 0;
if (l == r) return sg[id].cnt1;
int md = (l + r) >> 1;
return get(id << 1, l, md, pos) + get(id << 1 | 1, md + 1, r, pos);
}
int walk(int id, int l, int r, int val){
pus(id, l, r);
if (l == r) return l;
int md = (l + r) >> 1;
pus(id << 1, l, md);
pus(id << 1 | 1, md + 1, r);
if (sg[id << 1].cnt0 >= val) return walk(id << 1, l, md, val);
return walk(id << 1 | 1, md + 1, r, val - sg[id << 1].cnt0);
}
bool check(int x, int len){
int p = parent(x, len);
if (get(1, 1, n, ou[p])) return true;
return false;
}
void solve(){
cin >> n >> q;
int root = 0;
for (int i = 1; i <= n; ++i){
cin >> p[i];
g[p[i]].push_back(i);
if (!p[i]) root = i;
}
for (int i = 1; i <= n; ++i) sort(all(g[i]));
depth[root] = 1;
dfs(root);
build(1, 1, n);
build1();
while (q--){
int ty, x;
cin >> ty >> x;
if (ty == 1){
int d = walk(1, 1, n, x);
cout << getmin(1, d) << "\n";
update(1, 1, n, 1, d, 1);
}
else{
int l = 0, r = depth[x] - 1;
while (l < r){
int md = (l + r) >> 1;
if (check(x, md + 1)) l = md + 1;
else r = md;
}
cout << l << "\n";
int p = parent(x, l);
update(1, 1, n, ou[p], ou[p], 0);
}
}
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
// freopen(taskname".inp", "r", stdin);
// freopen(taskname".out", "w", stdout);
int tt = 1;
// cin >> tt;
while (tt--) solve();
}
