#include<bits/stdc++.h>
using namespace std;
using ll = long long;
ll n, Q;
ll p[200005];
vector<ll> ans;
struct st
{
ll t, x, y;
}qry[400005];
ll uf[200005];
ll Find(ll n)
{
if (uf[n] == -1) return n;
return uf[n] = Find(uf[n]);
}
void Union(ll x, ll y)
{
x = Find(x), y = Find(y);
uf[y] = x;
}
int main()
{
cin.tie(0); cout.tie(0);
ios_base::sync_with_stdio(false);
cin >> n >> Q;
fill(uf, uf + 200005, -1);
for (ll i = 2; i <= n; i++) cin >> p[i];
for (ll i = 1; i < n + Q; i++)
{
ll op; cin >> op;
if (op == 0)
{
ll x; cin >> x;
qry[i] = { 0, x, 0 };
}
else
{
ll x, y; cin >> x >> y;
qry[i] = { 1, x, y };
}
}
for (ll i = n + Q - 1; i >= 1; i--)
{
if (qry[i].t == 0) Union(qry[i].x, p[qry[i].x]);
else ans.push_back(Find(qry[i].x) == Find(qry[i].y));
}
reverse(ans.begin(), ans.end());
for (auto i : ans) cout << (i ? "YES\n" : "NO\n");
}
