#include <bits/stdc++.h>
using namespace std;
#define name "STEELWALL"
#define fi first
#define se second
#define int long long
#define endl '\n'
#define setmin(x, y) x = min((x), (y))
#define setmax(x, y) x = max((x), (y))
#define sqr(x) ((x) * (x))
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define trav(a, x) for(auto& a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
mt19937 hdp(chrono::high_resolution_clock::now().time_since_epoch().count());
int rand(int l, int r){return l + ((hdp() % (r - l + 1)) + r - l + 1) % (r - l + 1);}
const int NM = 1e5 + 5;
const int LG = 18;
const int inf = 1e9;
vector<int> g[NM];
int n, q, up[NM][LG], mn[2 * NM][LG + 1], a[NM], tin[NM], tout[NM], timer, d[NM], rt;
struct BIT
{
int dt[NM];
BIT(){memset(dt, 0, sizeof dt);}
void upd(int x, int v)
{
for (; x <= n; x += x & -x)
dt[x] += v;
}
void upd(int l, int r, int v)
{
upd(l, v);
upd(r + 1, -v);
}
int get(int x)
{
int res = 0;
for (; x; x -= x & -x)
res += dt[x];
return res;
}
}bit;
struct ST
{
pair<int, int> dt[4 * NM];
void build(int x = 1, int l = 1, int r = n)
{
if (l == r)
{
dt[x] = make_pair(inf, l);
return;
}
int m = l + r >> 1;
build(x << 1, l, m);
build(x << 1 | 1, m + 1, r);
dt[x] = min(dt[x << 1], dt[x << 1 | 1]);
}
void upd(int i, int x = 1, int l = 1, int r = n)
{
if (l == r)
{
dt[x].fi = inf + a[i] - dt[x].fi;
return;
}
int m = l + r >> 1;
if (m >= i)
upd(i, x << 1, l, m);
else
upd(i, x << 1 | 1, m + 1, r);
dt[x] = min(dt[x << 1], dt[x << 1 | 1]);
}
}st;
void dfs(int u)
{
tin[u] = ++timer;
mn[timer][0] = u;
for (int v : g[u])
dfs(v);
tout[u] = timer;
}
int par(int u, int k)
{
while (k)
{
u = up[u][__lg(k)];
k ^= (1 << __lg(k));
}
return u;
}
void solve()
{
cin >> n >> q;
for (int i = 1; i <= n; i++)
{
cin >> up[i][0];
if (up[i][0])
g[up[i][0]].push_back(i);
else
rt = i;
}
dfs(rt);
for (int j = 1; (1 << j) <= n; j++)
for (int i = 1; i <= n; i++)
up[i][j] = up[up[i][j - 1]][j - 1];
for (int j = 1; (1 << j) <= n; j++)
for (int i = 1; i + (1 << j) - 1 <= timer; i++)
mn[i][j] = min(mn[i][j - 1], mn[i + (1 << j - 1)][j - 1]);
for (int i = 1; i <= n; i++)
{
int l = tin[i], r = tout[i];
int L = __lg(r - l + 1);
a[i] = min(mn[l][L], mn[r - (1 << L) + 1][L]);
}
st.build();
for (int i = 1; i <= n; i++)
{
d[i] = g[i].size();
if (!d[i])
st.upd(i);
}
while (q--)
{
int op, t;
cin >> op >> t;
if (op == 1)
{
int u = 0;
while (t--)
{
u = st.dt[1].se;
st.upd(u);
bit.upd(tin[u], tout[u], 1);
d[up[u][0]]--;
if (up[u][0] && !d[up[u][0]])
st.upd(up[u][0]);
}
cout << u << endl;
}
else
{
int x = bit.get(tin[t]);
int u = par(t, x - 1);
bit.upd(tin[u], tout[u], -1);
d[up[u][0]]++;
st.upd(u);
cout << x - 1 << endl;
}
}
}
signed main()
{
if (fopen("in.txt", "r"))
{
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
}
else if (fopen(name".inp", "r"))
{
freopen(name".inp", "r", stdin);
freopen(name".out", "w", stdout);
}
ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
int tc = 1;
// cin >> tc;
while (tc--)
solve();
}
