#include<bits/stdc++.h>

using namespace std;

const int N = 1e5 + 5;
const int M = 2e3 + 5;

vector<int> g[N];
int n, k, id, mx, ans, maxx, col[N], f[N], dep[N], siz[N], dfn[N], c[M][M], d[M][M], cc[N], nw[M];

void dfs(int x, int fa){
  c[dep[x]][col[x]]++;
  mx = max(mx, dep[x]);
  dfn[x] = ++id, siz[x] = 1;
  for(int v : g[x]){
    if(v != fa){
      dep[v] = dep[x] + 1;
      dfs(v, x);
      siz[x] += siz[v];
    }
  }
}

void DFS(int x, int fa){
  for(int v : g[x]){
    if(v != fa) DFS(v, x);
  }
  for(int i = dep[x]; i <= mx; i++) nw[i] = 0;
  for(int i = 1; i <= n; i++){
    d[dep[i]][col[i]] = 0;
  }
  for(int i = 1; i <= n; i++){
    if(dfn[i] >= dfn[x] && dfn[i] <= dfn[x] + siz[x] - 1){
      nw[dep[i]]++;
      d[dep[i]][col[i]]++;
    }
  }
  int now = 1, sec = 0;
  for(int i = dep[x] + 1; i <= mx; i++){
    now += d[i][col[x]];
    int tmp = min(nw[i], c[i][col[x]]) - d[i][col[x]];
    now += tmp, sec += tmp;
  }
  if(now > ans) ans = now, maxx = sec;
  else if(now == ans) maxx = min(maxx, sec);
}

bool Check(){
  for(int i = 2; i <= n; i++){
    if(f[i] != i - 1) return 0;
  }
  return 1;
}

vector<int> ttt19;

bool Check2(){
  for(int i = 0; i <= k + 1; i++) ttt19.push_back(0);
  for(int i = 1; i <= n; i++){
    ttt19[col[i]]++;
    if(ttt19[col[i]] > 50) return 0;
  }
  return 1;
}

vector<int> dd[N], ccc[N];

void DD(int x, int fa){
  dep[x] = dep[fa] + 1;
  dfn[x] = ++id, siz[x] = 1;
  dd[dep[x]].push_back(dfn[x]);
  ccc[col[x]].push_back(x);
  for(int v : g[x]){
    if(v != fa){
      DD(v, x);
      siz[x] += siz[v];
    }
  }
}

int query(int id, int l, int r){
  return upper_bound(dd[id].begin(), dd[id].end(), r) - lower_bound(dd[id].begin(), dd[id].end(), l);
}

int t64[N];

void Solve(){
  DD(1, 0);
  ans = -1;
  for(int i = 0; i <= k; i++){
    for(int u : ccc[i]){
      int now = 0, sec = 0;
      for(int v : ccc[i]){
        t64[dep[v]] = query(dep[v], dfn[u], dfn[u] + siz[u] - 1);
      }
      for(int v : ccc[i]){
        if(t64[dep[v]]){
          now++;
          if(dfn[v] < dfn[u] || dfn[v] > dfn[u] + siz[u] - 1) t64[dep[v]]--, sec++;
        }
      }
      if(now > ans) ans = now, maxx = sec;
      else if(now == ans) maxx = min(maxx, sec);
    }
  }
  cout << ans << ' ' << maxx;
}

int main(){
  ios::sync_with_stdio(0), cin.tie(0);
  cin >> n >> k;
  for(int i = 1; i <= n; i++) cin >> col[i];
  for(int i = 2; i <= n; i++){
    cin >> f[i];
    g[++f[i]].push_back(i);
  }
  if(Check()){
    for(int i = n; i >= 1; i--){
      cc[col[i]]++;
      ans = max(ans, cc[col[i]]);
    }
    cout << ans << ' ' << 0;
    return 0;
  }
  if(Check2()){
    Solve();
    return 0;
  }
  ans = -1;
  dfs(1, 0);
  DFS(1, 0);
  cout << ans << ' ' << maxx;
  return 0;
}