#include <bits/stdc++.h>
using namespace std;
#define name "BALLMACHINE"
#define endl '\n'
#define ednl endl
#define long long long
#define memset(a, x) memset(a, (x), sizeof(a));
#define inoutf freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout);
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define IN(a, b, c) (a <= b && b <= c)
template<typename T, typename U> inline bool amin(T &x, U y) { if(y >= x) return 0; x = y; return 1;}
template<typename T, typename U> inline bool amax(T &x, U y) { if(x >= y) return 0; x = y; return 1;}
template<typename T> inline void read(T& x){
bool Neg = false;
char c;
for (c = getchar(); c < '0' | c > '9'; c = getchar())
if (c == '-') Neg = !Neg;
x = c - '0';
for (c = getchar(); c >= '0' && c <= '9'; c = getchar())
x = x * 10 + c - '0';
if (Neg) x = -x;
}
const int N = 1e5 + 83;
vector <int> Graph[N];
int Min[N], Priority[N], cnt = 0, pa[N][30], h[N], rePriority[N];
bool Have[N];
bool comp(int a, int b){
return Min[a] < Min[b];
}
int dfs(bool sta, int u, int pa){
if (sta && pa != -1) h[u] = h[pa] + 1;
Min[u] = u;
for (int &v : Graph[u]){
amin(Min[u], dfs(sta, v, u));
}
if (sta){
Priority[++cnt] = u;
rePriority[u] = cnt;
}
return Min[u];
}
struct segtree{
int Size;
vector <int> ord;
void init(int n){
Size = n;
ord.assign(4 * n, 0);
}
void update(int &i, int &p, int x, int lx, int rx){
if (lx == rx){
ord[x] = p;
return;
}
int mid = (lx + rx) >> 1;
if (mid < i) update(i, p, x << 1 | 1, mid + 1, rx);
else update(i, p, x << 1, lx, mid);
ord[x] = ord[x << 1] + ord[x << 1 | 1];
}
void update(int i, int p){update(i, p, 1, 1, Size);}
int get_prio(int k, int x, int lx, int rx){
if (lx == rx) return Priority[lx];
int mid = (lx + rx) >> 1;
if (ord[x << 1] < k) return get_prio(k - ord[x << 1], x << 1 | 1, mid + 1, rx);
return get_prio(k, x << 1, lx, mid);
}
int get_prio(int k){return get_prio(k, 1, 1, Size);}
}st;
int LCA(int u){
int log = log2(h[u]);
for (int i = log; i >= 0; --i){
if (pa[u][i] != -1 && Have[pa[u][i]]) u = pa[u][i];
}
return u;
}
int Solve(){
int n, q; cin >> n >> q;
memset(pa, -1);
for (int i = 1; i <= n; ++i){
cin >> pa[i][0];
Graph[pa[i][0]].push_back(i);
}
dfs(0, 0, -1);
for (int i = 1; i <= n; ++i){
sort(Graph[i].begin(), Graph[i].end(), comp);
}
h[0] = 0;
dfs(1, 0, -1);
memset(Have, 0);
st.init(n);
for (int i = 1; i <= n; ++i) st.update(i, 1);
int log = log2(n);
for (int j = 1; j <= log; ++j){
for (int i = 1; i <= n; ++i){
if (pa[i][j - 1] == -1) continue;
pa[i][j] = pa[pa[i][j - 1]][j - 1];
}
}
while (q--){
int sta, x; cin >> sta >> x;
switch (sta){
case 1:{
int last;
while(x--){
last = st.get_prio(1);
Have[last] = 1;
st.update(rePriority[last], 0);
}
cout << last << endl;
break;
}
case 2:{
int farPa = LCA(x);
cout << h[x] - h[farPa] << endl;
st.update(rePriority[farPa], 1);
Have[farPa] = 0;
break;
}
}
}
return 0;
}
int main(){
fastio;
int t = 1;
// cin >> t;
while (t--){
Solve();
}
return 0;
}
