/<> 13306

#include <iostream>
#include <string>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <deque>
#include <unordered_map>
#include <numeric>
#include <iomanip>
using namespace std;
#define pii pair<int , int>
#define ll long long
#define FAST ios_base::sync_with_stdio(false); cin.tie(NULL)
const long long dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
const long long dl[2] = {1, -1};
const long long MOD = 1000000007;
const long long MAXN = 200005;

int N, Q, par[MAXN], p[MAXN], sz[MAXN];
vector<pair<int, pii>> q;
vector<string> ans;

int Find(int x){
    if(x == p[x]) return x;
    return p[x] = Find(p[x]);
}
void Union(int a, int b){
    a = Find(a); b = Find(b);
    if(a == b) return;
    if(sz[a] > sz[b]) swap(a, b);
    p[a] = b;
    sz[b] += sz[a];
}
string Check(int a, int b){
    if(Find(a) == Find(b)){
        return "YES";
    }
    else{
        return "NO";
    }
}
void init(){
    for(int i = 1; i <= N; i++){
        p[i] = i;
        sz[i] = 1;
    }
}

int main() {
    FAST;
    cin >> N >> Q;
    for(int i = 2; i <= N; i++){
        cin >> par[i];
    }
    init();
    for(int x, y, z, i = 0; i < N + Q - 1; i++){
        cin >> x;
        if(x == 0){
            cin >> y;
            q.push_back({x, {y, -1}});
        }
        else{
            cin >> y >> z;
            q.push_back({x, {y, z}});
        }
    }
    reverse(q.begin(), q.end());
    for(auto x : q){
        if(x.first == 0){
            Union(x.second.first, par[x.second.first]);
        }
        else{
            ans.push_back(Check(x.second.first, x.second.second));
        }
    }
    reverse(ans.begin(), ans.end());
    for(auto x : ans){
        cout << x << "\n";
    }
}

/*
11 5
7
4
1
9
11
1
11
1
3
7
0 11
1 8 5
1 3 9
0 10
0 9
0 7
1 2 7
0 5
1 1 10
0 8
0 6
0 2
1 1 3
0 3
0 4
 */