#include <stdio.h>
#include <bits/stdc++.h>
using namespace std;
#define SZ(v) ((int)(v).size())
#define ALL(v) (v).begin(),(v).end()
#define one first
#define two second
typedef long long ll;
typedef pair<double, double> pd;
typedef pair<int, int> pi; typedef pair<ll, int> pli;
typedef pair<ll, ll> pll; typedef pair<ll, pi> plp;
typedef tuple<int, int, int> ti; typedef tuple<ll, int, int> tli;
const int INF = 0x3f2f1f0f;
const ll LINF = 1ll * INF * INF;
const int MAX_N = 2e5 + 100, MAX_Q = 2e5 + 100, LOG_N = 21;
int N, Q, iP[MAX_N];
vector<int> Ed[MAX_N];
int P[LOG_N][MAX_N], D[MAX_N], S[MAX_N];
int predfs(int v, int p) {
D[v] = D[p] + 1; S[v] = 1; P[0][v] = p;
for(int w : Ed[v]) if(w != p) S[v] += predfs(w, v);
return S[v];
}
struct BIT {
int val[MAX_N];
BIT() {memset(val, 0, sizeof(val));}
void update(int v, int k) {for(v+=10; v<MAX_N; v+=v&-v) val[v]+=k;}
int getSum(int v) {int res=0; for(v+=10; v; v-=v&-v) res+=val[v]; return res;}
int getSum(int a, int b) {return getSum(b) - getSum(a-1);}
}bit;
int eN = 0;
int eIx[MAX_N], fIx[MAX_N];
void makedfs(int v, int p, int h) {
// printf("%d %d %d\n", v, p, h);
if(v != N/2) bit.update(eN, 1), eIx[v] = eN++; fIx[v] = h;
int ix = -1;
for(int w : Ed[v]) if(w != p && (ix == -1 || S[ix] < S[w])) ix = w;
if(ix == -1) return;
makedfs(ix, v, h);
for(int w : Ed[v]) if(w != p && w != ix) makedfs(w, v, w);
}
int getL(int a, int b) {
if(D[a] > D[b]) swap(a, b);
for(int p=LOG_N-1; p>=0; p--) if((D[b]-D[a])&(1<<p)) b=P[p][b];
if(a == b) return a;
for(int p=LOG_N-1; p>=0; p--) if(P[p][a]!=P[p][b]) a=P[p][a], b=P[p][b];
return P[0][a];
}
bool isCan(int fr, int to) {
int hd = fIx[fr];
if(D[to] < D[hd]) {
int val = bit.getSum(eIx[hd], eIx[fr]);
if(val != D[fr] - D[hd] + 1) return false;
return isCan(P[0][hd], to);
} else {
int val = bit.getSum(eIx[fr] - (D[fr] - D[to]) + 1, eIx[fr]);
return val == (D[fr] - D[to]);
}
printf("what?\n");
return false;
}
int main() {
cin >> N >> Q;
for(int i=2; i<=N; i++) scanf("%d", &iP[i]);
for(int i=2; i<=N; i++) Ed[i].push_back(iP[i]), Ed[iP[i]].push_back(i);
predfs(N/2, 0);
for(int p=1; p<LOG_N; p++) for(int i=1; i<=N; i++) P[p][i] = P[p-1][P[p-1][i]];
makedfs(N/2, 0, N/2);
for(int q=1; q<=Q; q++) {
int b, c, d; scanf("%d%d%d", &b, &c, &d);
int l = getL(b, c);
// printf("[%d %d -> %d]\n", b, c, l);
// printf("b %d | c %d\n", isCan(b, l), isCan(c, l));
bool ans = (isCan(b, l) & isCan(c, l));
puts(ans?"YES":"NO");
if(d == 1) {
int x = b, y = iP[b];
if(!ans) x = c, y = iP[c];
if(x == 1) continue;
if(D[x] > D[y]) swap(x, y);
if(bit.getSum(eIx[y], eIx[y]) == 0) continue;
bit.update(eIx[y], -1);
}
}
return 0;
}
