#include<bits/stdc++.h>

using namespace std;

const int N = 1e5 + 5, B = 320;

int _sum, dep[N], dfn[N], tot, n, k, cnt[N], c[N], sum[N], ans[N], xa, xb, End[N], pp, _cnt[N], p[N], u;
vector<int>v1[N], v2[N], g[N], e[N];

void Mr(vector<int>&a, vector<int>&b){
  if(b.size() > a.size()){
    swap(a, b);
  }
  for(int i = 0; i < b.size(); i++){
    a[a.size() - i - 1] = a[a.size() - i - 1] + b[b.size() - i - 1];
  }
}

void dfs(int x, int fa){
  v1[x].clear(), v2[x].clear();
  for(auto v : g[x]){
    dfs(v, x);
    Mr(v1[x], v1[v]);
  }
  v1[x].push_back(1);
  if(cnt[c[x]] <= B){
    pp = 0;
    vector<int>ev;
    for(auto v : e[c[x]]){
      if(dfn[v] >= dfn[x] && dfn[v] <= End[x]){
       pp++;
      }
      if(dep[v] >= dep[x]){
        ev.push_back(dep[v]);
        _cnt[dep[v]]++;
      }
    }
    sort(ev.begin(), ev.end());
    ev.erase(unique(ev.begin(), ev.end()), ev.end());
    _sum = 0;
    for(auto v : ev){
      if(v1[x].size() - (v - dep[x]) - 1 >= 0){
        _sum += min(_cnt[v], v1[x][int(v1[x].size()) - (v - dep[x]) - 1]);
      }
      _cnt[v] = 0;
    }
    if(_sum > xa || _sum == xa && xb > _sum - pp){
      xa = _sum, xb = _sum - pp;
    }
  }
}

void DFS(int x, int id){
  v1[x].clear(), v2[x].clear(), sum[x] = 0, ans[x] = 0;
  for(auto v : g[x]){
    DFS(v, id);
    if(v1[x].size() < v1[v].size()){
      swap(v1[x], v1[v]);
      swap(v2[x], v2[v]);
      swap(ans[x], ans[v]);
      swap(sum[x], sum[v]);
    }
    for(int i = 0; i < v1[v].size(); i++){
      ans[x] -= v1[x][int(v1[x].size()) - i - 1] - v2[x][int(v1[x].size()) - i - 1];
      sum[x] -= v1[x][int(v1[x].size()) - i - 1];
    }
    for(int i = 0; i < v1[v].size(); i++){
      v1[x][int(v1[x].size()) - i - 1] = min(v1[x][int(v1[x].size()) - i - 1] + v1[v][int(v1[v].size()) - i - 1], p[dep[x] + i + 1]);
      v2[x][int(v1[x].size()) - i - 1] += v2[v][int(v1[v].size()) - i - 1];
    }
    for(int i = 0; i < v1[v].size(); i++){
      ans[x] += v1[x][int(v1[x].size()) - i - 1] - v2[x][int(v1[x].size()) - i - 1];
      sum[x] += v1[x][int(v1[x].size()) - i - 1];
    }
  }
  v1[x].push_back(min(1, p[dep[x]]));
  v2[x].push_back(c[x] == id);
  ans[x] += v1[x].back() - v2[x].back();
  sum[x] += v1[x].back();
  if((c[x] == id) && (sum[x] > xa || sum[x] == xa && xb > ans[x])){
    xa = sum[x], xb = ans[x];
  }
}

void Dfs(int x, int fa){
  dep[x] = dep[fa] + 1;
  dfn[x] = ++tot;
  for(auto v : g[x]){
    Dfs(v, x);
  }
  End[x] = tot;
}

signed main(){
  cin >> n >> k;
  for(int i = 1; i <= n; ++i){
    cin >> c[i];
    c[i]++;
    cnt[c[i]]++;
    e[c[i]].push_back(i);
  }
  for(int i = 2; i <= n; ++i){
    cin >> u;
    g[u + 1].push_back(i);
  }
  Dfs(1, 0);
  dfs(1, 0);
  for(int i = 1; i <= k; ++i){
    if(cnt[i] > B){
      for(auto v : e[i]){
        p[dep[v]]++;
      }
      DFS(1, i);
      for(auto v : e[i]){
        p[dep[v]] = 0;
      }
    }
  }
  cout << xa << ' ' << xb << '\n';
  return 0;
}