#include <bits/stdc++.h>
using namespace std;
template<typename T>
int SIZE(T (&t)){
    return t.size();
}

template<typename T, size_t N>
int SIZE(T (&t)[N]){
    return N;
}

string to_string(char t){
    return "'" + string({t}) + "'";
}

string to_string(bool t){
    return t ? "true" : "false";
}

string to_string(const string &t, int x1=0, int x2=1e9){
    string ret = "";
    for(int i = min(x1,SIZE(t)), _i = min(x2,SIZE(t)-1); i <= _i; ++i){
        ret += t[i];
    }
    return '"' + ret + '"';
}

string to_string(const char* t){
    string ret(t);
    return to_string(ret);
}

template<size_t N>
string to_string(const bitset<N> &t, int x1=0, int x2=1e9){
    string ret = "";
    for(int i = min(x1,SIZE(t)); i <= min(x2,SIZE(t)-1); ++i){
        ret += t[i] + '0';
    }
    return to_string(ret);
}

template<typename T, typename... Coords>
string to_string(const T (&t), int x1=0, int x2=1e9, Coords... C);

template<typename T, typename S>
string to_string(const pair<T, S> &t){
    return "(" + to_string(t.first) + ", " + to_string(t.second) + ")";
}

template<typename T, typename... Coords>
string to_string(const T (&t), int x1, int x2, Coords... C){
    string ret = "[";
    x1 = min(x1, SIZE(t));
    auto e = begin(t);
    advance(e,x1);
    for(int i = x1, _i = min(x2,SIZE(t)-1); i <= _i; ++i){
        ret += to_string(*e, C...) + (i != _i ? ", " : "");
        e = next(e);
    }
    return ret + "]";
}

template<int Index, typename... Ts>
struct print_tuple{
    string operator() (const tuple<Ts...>& t) {
        string ret = print_tuple<Index - 1, Ts...>{}(t);
        ret += (Index ? ", " : "");
        return ret + to_string(get<Index>(t));
    }
};

template<typename... Ts>
struct print_tuple<0, Ts...> {
    string operator() (const tuple<Ts...>& t) {
        return to_string(get<0>(t));
    }
};

template<typename... Ts>
string to_string(const tuple<Ts...>& t) {
    const auto Size = tuple_size<tuple<Ts...>>::value;
    return print_tuple<Size - 1, Ts...>{}(t);
}

void dbgr(){;}
template<typename Heads, typename... Tails>
void dbgr(Heads H, Tails... T){
    cout << to_string(H) << " | ";
    dbgr(T...);
}

void dbgs(){;}
template<typename Heads, typename... Tails>
void dbgs(Heads H, Tails... T){
    cout << H << " ";
    dbgs(T...);
}

/*
formatted functions:
*/

/*
consider __VA_ARGS__ as a whole:
dbgv() prints values only
dbg() prints name and values
*/
#define dbgv(...) cout << to_string(__VA_ARGS__) << endl;

#define dbg(...) cout << "[" << #__VA_ARGS__ << "]: "; dbgv(__VA_ARGS__);
//#define dbg(...)

/*
consider __VA_ARGS__ as a sequence of arguments:
dbgr() prints values only
dbgm() prints names and values
*/
#define dbgr(...) dbgr(__VA_ARGS__); cout << endl;

#define dbgm(...) cout << "[" << #__VA_ARGS__ << "]: "; dbgr(__VA_ARGS__);

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
typedef pair<int, int> pi;
typedef pair<ll, ll> pll;
// using u128 = __uint128_t;
// using i128 = __int128;
const int mod = 1000000007;
const int N = 200005;
const int LOG = 20;
const int inf = 1e9;
const double eps = 1e-11;
int n, m, k, qq;
vector<int> adj[N];
int p[N], c[N], sub[N];
vector<int> f;
map<int, int> cnt[N];
set<pi> g[N];
bool ins(int u, set<pi> &s) {
    auto it = s.lower_bound({sub[u], 0});
    if (it != s.end()) {
        auto [sz, v] = *it;
        assert(sub[v] >= sub[u]);
        for (auto [cc, cntc] : cnt[u]) {
            int ccc = cnt[v][cc];
            if (cntc > ccc) return 0;
        }
    }
    
    if (it != s.begin()) {
        it--;
        auto [sz, v] = *it;
        assert(sub[v] < sub[u]);
        int amt = 0;
        for (auto [cc, cntc] : cnt[u]) {
            // dbgm(cc, cntc, cnt[v][cc]);
            int ccc = cnt[v][cc];
            if (cntc < ccc) return 0;
            amt += ccc;
        }
        
        if (amt < sub[v] - 1) return 0;
    }
    
    s.insert({sub[u], u});
    return 1;
}

void dfs(int u) {
    for (int v : adj[u]) {
        dfs(v);
        sub[u] += sub[v], cnt[u][c[v]] += sub[v];
    }

    g[u].insert({sub[u], u});
    set<int> colours;
    for (int v : adj[u]) {
        if (colours.contains(c[v])) {
            f[u] = 0;
            return;    
        }
        
        colours.insert(c[v]);
        if (g[u].size() < g[v].size()) swap(g[u], g[v]);
        for (auto [t, w] : g[v]) {
            if (!ins(w, g[u])) {
                // dbgm(u, "AAAHs", w);
                // dbg(g[u]);
                f[u] = 0;
                return;
            }
        }
    }
}

// std::vector<int> beechtree(int NN, int MM, std::vector<int> P, std::vector<int> C) {
//     n = NN, m = MM;
//     f = vector<int>(n, 1);
//     for (int i = 1; i < n; i++) {
//         adj[P[i]].push_back(i);
//     }
    
//     for (int i = 0; i < n; i++) {
//         p[i] = P[i], c[i] = C[i], sub[i] = 1;
//     }
    
//     dfs(0);
//     return f;
// }

// void solve() {
//     int N, M;
//     assert(2 == scanf("%d %d", &N, &M));
//     std::vector<int> P(N);
//     for (int i = 0; i < N; ++i)
//         assert(1 == scanf("%d", &P[i]));
//     std::vector<int> C(N);
//     for (int i = 0; i < N; ++i)
//         assert(1 == scanf("%d", &C[i]));

//     fclose(stdin);

//     std::vector<int> res = beechtree(N, M, P, C);

//     int n = res.size();
//     for (int i = 0; i < n; ++i)
//     {
//         if (i > 0)
//             printf(" ");
//         printf("%d", res[i]);
//     }
//     printf("\n");
//     fclose(stdout);
// }

// int32_t main() {
//     // std::ios::sync_with_stdio(false);
//     // cin.tie(NULL);
//     solve();
// }

/usr/bin/ld: /tmp/ccxuCasC.o: in function `main':
implementer.cpp:(.text.startup+0x27d): undefined reference to `beechtree(int, int, std::vector<int, std::allocator<int> >, std::vector<int, std::allocator<int> >)'
collect2: error: ld returned 1 exit status