#include "bits/stdc++.h"
using namespace std;
#ifdef duc_debug
#include "bits/debug.h"
#else
#define debug(...)
#endif
const int maxn = 1e5 + 5;
const int LG = 18;
int n, q, root;
vector<int> g[maxn];
int h[maxn], par[maxn];
int tin[maxn], tout[maxn], timer, et[maxn];
int up[maxn][LG + 1];
int mvt[maxn];
void pre_dfs(int u) {
mvt[u] = u;
for (auto v : g[u]) {
h[v] = h[u] + 1;
up[v][0] = u;
for (int i = 1; i <= LG; ++i) {
up[v][i] = up[up[v][i - 1]][i - 1];
}
pre_dfs(v);
mvt[u] = min(mvt[u], mvt[v]);
}
sort(g[u].begin(), g[u].end(), [](const int &x, const int &y) -> bool {
return mvt[x] < mvt[y];
});
}
void dfs(int u) {
tin[u] = timer;
for (auto v : g[u]) {
dfs(v);
}
tout[u] = ++timer;
et[timer] = u;
}
int bit[maxn];
void upd(int i, int val) {
val = -val;
for (; i <= n; i += i & (-i)) {
bit[i] += val;
}
}
int lower_bound(long long v) {
long long sum = 0;
int pos = 0;
for (int i = LG; i >= 0; i--) {
if (pos + (1 << i) <= n and sum + bit[pos + (1 << i)] < v) {
sum += bit[pos + (1 << i)];
pos += (1 << i);
}
}
return pos + 1;
}
int get(int i) {
int ans = 0;
for (; i > 0; i -= i & (-i)) {
ans += bit[i];
}
return ans;
}
void solve() {
cin >> n >> q;
for (int i = 1; i <= n; ++i) {
cin >> par[i];
if (par[i] == 0) root = i;
else g[par[i]].push_back(i);
}
pre_dfs(root);
dfs(root);
for (int i = 1; i <= n; ++i) {
upd(i, -1);
}
while (q--) {
int op; cin >> op;
if (op == 1) {
int k; cin >> k;
int cur = 0;
for (int i = 1; i <= k; ++i) {
cur = lower_bound(1);
upd(cur, 1);
}
cout << et[cur] << '\n';
} else {
int u; cin >> u;
int res = 0;
for (int i = LG; i >= 0; --i) {
if (up[u][i] and get(tout[up[u][i]]) == get(tout[up[u][i]] - 1)) {
res ^= (1 << i);
u = up[u][i];
}
}
upd(tout[u], -1);
cout << res << '\n';
}
}
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
solve();
return 0;
}
