#include <bits/stdc++.h>
using namespace std;
typedef pair<int, int> p;
template <typename T>
class SegTree{
private:
T tree[808080];
int lim;
function<T(const T a, const T b)> f;
public:
void init(int n, function<T(const T a, const T b)> func){
f = func;
for(lim = 1; lim <= n; lim <<= 1);
}
void update(int x, T v){
x += lim;
tree[x] = v;
while(x > 1){
x >>= 1;
tree[x] = f(tree[2*x], tree[2*x+1]);
}
}
T query(int s, int e){
s += lim;
e += lim;
T ret = 1;
while(s < e){
if(s%2 == 1) ret = f(ret, tree[s++]);
if(e%2 == 0) ret = f(ret, tree[e--]);
s >>= 1;
e >>= 1;
}
if(s == e) ret = f(ret, tree[s]);
return ret;
}
};
template <typename T>
class HLD{
private:
int dn;
int par[202020], size[202020], depth[202020], lab[202020];
int id[202020], top[202020];
SegTree<T> tree;
function<T(const T a, const T b)> f;
int dfs(int now, int prv){
par[now] = prv; size[now] = 1;
for(auto &t: g[now]){
int nxt = t.first;
if(nxt != prv){
depth[nxt] = depth[now] + 1;
size[now] += dfs(nxt, now);
}
}
return size[now];
}
void decom(int now, int prv, int chain){
lab[now] = dn;
id[dn] = chain;
top[chain] = dn++;
int heavy = -1;
for(auto &t: g[now]){
int nxt = t.first;
if(nxt != prv && (heavy == -1 || size[nxt] > size[heavy])) heavy = nxt;
}
if(heavy != -1) decom(heavy, now, chain);
for(auto &t: g[now]){
int nxt = t.first;
if(nxt != prv && nxt != heavy) decom(nxt, now, nxt);
}
}
public:
vector<p> g[202020];
void init(int root, function<T(const T a, const T b)> func){
//init value
f = func;
dn = 0;
memset(id,-1,sizeof(id));
memset(top,-1,sizeof(top));
//pre-processing
dfs(root,-1);
decom(root,-1,root);
//set edge's weight
vector<T> a(202020);
for(int i=0;i<202020;i++){
for(auto &t: g[i]){
int next = t.first, w = t.second;
int v = lab[next];
if(depth[i] < depth[next]) a[v] = w;
}
}
tree.init(a.size(), f);
for(int i=0; i<a.size(); i++) tree.update(i, a[i]);
}
void update(int u, int v, T k){
if(depth[u] < depth[v]) swap(u, v);
tree.update(lab[u], k);
}
T query(int u, int v){
T ret = 1;
u = lab[u], v = lab[v];
while(id[u] != id[v]){
int uHead = id[u], vHead = id[v];
if(depth[uHead] > depth[vHead]){
ret = f(ret, tree.query(lab[uHead], u));
u = lab[par[uHead]];
}
else{
ret = f(ret,tree.query(lab[vHead], v));
v = lab[par[vHead]];
}
}
ret = f(ret, tree.query(min(u, v)+1, max(u,v)));
return ret;
}
};
HLD<int> hld;
vector<int> par(202020);
int main(){
ios_base::sync_with_stdio(0); cin.tie(0);
int n, q; cin >> n >> q;
for(int i=2; i<=n; i++){
int t; cin >> t;
par[i] = t;
hld.g[t].push_back({i, 1});
}
hld.init(1, [](int a, int b){
return a && b;
});
while(q--){
int a, b, op; cin >> a >> b >> op;
int res = hld.query(a, b);
if(res) cout << "YES\n";
else cout << "NO\n";
if(op == 1){
if(res) hld.update(a, par[a], 0);
else hld.update(b, par[b], 0);
}
}
}
