#include <stdio.h>
#include <vector>
#define NN 262144
#define INF 999999999
using namespace std;
struct Node {
int s, e, up;
} node[200001];
vector<int> r[200001];
int n, nn, q, tree_cnt, tree[NN * 2];
int max2(int x, int y) { return x > y ? x : y; }
void make_tree(int x, int up) {
node[x].up = up, node[x].s = ++tree_cnt;
for (auto i : r[x])
if (i != up) make_tree(i, x);
node[x].e = tree_cnt;
}
int get_top(int x) {
if (x == 1) return tree[1];
return max2(tree[x], get_top(x / 2));
}
void tree_push(int lev, int l, int r, int x, int y, int num) {
int mid = (l + r) / 2;
if (x <= l && r <= y) { tree[lev] = max2(tree[lev], num); return; }
if (r < x || y < l) return;
tree_push(lev * 2, l, mid, x, y, num), tree_push(lev * 2 + 1, mid + 1, r, x, y, num);
}
int main() {
int x, y, z;
scanf("%d %d", &n, &q);
for (nn = 1; nn < n; nn *= 2);
for (int i = 2; i <= n; i++) {
scanf("%d", &x);
r[i].push_back(x), r[x].push_back(i);
}
make_tree(1, 0), tree[1] = 1;
while (q--) {
scanf("%d %d %d", &x, &y, &z);
int tx = get_top(node[x].s + nn - 1), ty = get_top(node[y].s + nn - 1);
printf("%s\n", tx == ty ? "YES" : "NO");
if (z && tx == ty) tree_push(1, 1, nn, node[x].s, node[x].e, node[x].s);
if (z && tx != ty) tree_push(1, 1, nn, node[y].s, node[y].e, node[y].s);
}
}
