#include<bits/stdc++.h>
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL);
#define a first
#define b second
using namespace std;
const int MAXN = 2 * 1e6 + 1;
typedef pair<pair<int, int>, pair<int, int>> pai;
int n, q, parent[MAXN], fparent[MAXN], lvl[MAXN];
vector<pai> v;
stack<string> st;
int find(int u) {
    if (u == parent[u]) return u;
    return parent[u] = find(parent[u]);
}
void merge(int u, int v) {
    u = find(u);
    v = find(v);
    if (u == v) return;
    if (lvl[u] > lvl[v]) swap(u, v);
    parent[u] = v;
    lvl[v] += lvl[u];
}
int main() {
    fastio;
    cin >> n >> q;
    for (int i = 1; i <= n; i++) {
        parent[i] = i;
        lvl[i] = 1;
    }
    for (int i = 2; i <= n; i++) cin >> fparent[i];
    fparent[1] = 1;
    for (int x, a, b, i = 0; i < n - 1 + q; i++) {
        cin >> x;
        if (!x) {
            cin >> a;
            v.push_back({ {x,a},{0,0} });
        }
        else {
            cin >> a >> b;
            v.push_back({ {x,0},{a,b} });
        }
    }
    std::reverse(v.begin(), v.end());
    for (int i = 0; i < v.size(); i++) {
        int x = v[i].a.a;
        if (x == 0) {
            int k = v[i].a.b;
            merge(k, fparent[k]);
        }
        else {
            int k1 = find(v[i].b.a), k2 = find(v[i].b.b);
            if (k1 == k2) st.push("YES");
            else st.push("NO");
        }
    }
    while (!st.empty()) {
        cout << st.top() << "\n";
        st.pop();
    }
}