#include <bits/stdc++.h>
using namespace std;
int N, Q;
int cnt = 0;
vector<int> T[200005];
int in[200005];
int out[200005];
int seg[800005];
void update(int node, int s, int e, int l, int r, int v)
{
if(l <= s && e <= r) {seg[node] = max(seg[node], v); return;}
else if(s > r || e < l) return;
update(node * 2, s, (s + e) / 2, l, r, v);
update(node * 2 + 1, (s + e) / 2 + 1, e, l, r, v);
}
int query(int node, int s, int e, int k)
{
if(s == e) return seg[node];
int m = (s + e) / 2;
if(k <= m) return max(seg[node], query(node * 2, s, m, k));
else return max(seg[node], query(node * 2 + 1, m + 1, e, k));
}
void dfs(int n)
{
in[n] = ++cnt;
for(auto i : T[n]) dfs(i);
out[n] = cnt;
}
int main()
{
cin.tie(0); cout.tie(0);
ios_base::sync_with_stdio(false);
cin >> N >> Q;
for(int i = 2; i <= N; i++)
{
int u; cin >> u;
T[u].push_back(i);
}
dfs(1);
while(Q--)
{
int x, y, op; cin >> x >> y >> op;
if(op == 0) cout << (query(1, 1, N, in[x]) == query(1, 1, N, in[y]) ? "YES" : "NO") << '\n';
else
{
if(query(1, 1, N, in[x]) == query(1, 1, N, in[y])) cout << "YES\n";
else{cout << "NO\n"; swap(x, y);}
update(1, 1, N, in[x], out[x], in[x]);
}
}
}
