#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
vector<vector<ll>> edges;
vector<ll> pref;
ll n, k, timer = 0, tin[100005], tout[100005], depth[100005];
unordered_map<ll, ll> stuff[100005];
vector<ll> depths[100005], consider, prefs[100005];
ll ans = -1, ans2 = 0;
void dfs(ll a, ll d)
{
depths[d].push_back(a);
depth[a] = d;
stuff[d][pref[a]] += 1;
tin[a] = timer;
timer += 1;
for (auto &i : edges[a])
dfs(i, d + 1);
tout[a] = timer;
}
ll numchild(ll a, ll k)
{
if (!(0 <= k && k < 100005))
return 0;
vector<ll> &sus = depths[k];
if (sus.size() == 0)
return 0;
if (depth[a] == k)
return 0;
ll lo = 0;
ll hi = sus.size() - 1;
while (lo < hi)
{
ll mid = (lo + hi) / 2;
if (tin[sus[mid]] >= tin[a])
hi = mid;
else
lo = mid + 1;
}
ll leftp = lo;
lo = 0;
hi = sus.size() - 1;
while (lo < hi)
{
ll mid = (lo + hi + 1) / 2;
if (tout[sus[mid]] <= tout[a])
lo = mid;
else
hi = mid - 1;
}
ll rightp = lo;
if (!(tin[a] <= tin[sus[leftp]] && tout[sus[leftp]] <= tout[a]))
return 0;
return max((ll)0, rightp - leftp + 1);
}
ll numspecialchild(ll a, ll k, ll c)
{
if (!(0 <= k && k < 100005))
return 0;
vector<ll> &sus = depths[k];
if (sus.size() == 0)
return 0;
if (depth[a] == k)
return 0;
ll lo = 0;
ll hi = sus.size() - 1;
while (lo < hi)
{
ll mid = (lo + hi) / 2;
if (tin[sus[mid]] >= tin[a])
hi = mid;
else
lo = mid + 1;
}
ll leftp = lo;
lo = 0;
hi = sus.size() - 1;
while (lo < hi)
{
ll mid = (lo + hi + 1) / 2;
if (tout[sus[mid]] <= tout[a])
lo = mid;
else
hi = mid - 1;
}
ll rightp = lo;
ll ans = 0;
if (!(tin[a] <= tin[sus[leftp]] && tout[sus[leftp]] <= tout[a]))
return 0;
for (ll i = leftp; i < rightp + 1; i++)
{
ans += (pref[sus[i]] == c);
}
return ans;
}
void solve(ll a)
{
ll tans = 1;
ll tans2 = 0;
for (auto &i : consider)
{
ll temp = numchild(a, i);
if (temp == 0)
continue;
tans += min(temp, stuff[i][pref[a]]);
tans2 += min(temp, stuff[i][pref[a]]) - numspecialchild(a, i, pref[a]);
}
if (tans > ans)
ans = tans, ans2 = tans2;
else if (tans == ans)
ans2 = min(ans2, tans2);
}
void solve2(ll a)
{
ll tans = 1;
ll tans2 = 0;
for (ll i = depth[a] + 1; i < n; i++)
{
ll temp = numchild(a, i);
if (temp == 0)
break;
tans += min(temp, stuff[i][pref[a]]);
tans2 += min(temp, stuff[i][pref[a]]) - numspecialchild(a, i, pref[a]);
}
if (tans > ans)
ans = tans, ans2 = tans2;
else if (tans == ans)
ans2 = min(ans2, tans2);
}
void dfs2(ll a, ll p)
{
if (pref[a] == p)
{
solve2(a);
return;
}
for (auto &i : edges[a])
dfs2(i, p);
}
int main()
{
for (ll i = 0; i < 100005; i++)
{
stuff[i].reserve(1 << 10);
stuff[i].max_load_factor(0.25);
}
scanf("%lld %lld", &n, &k);
for (ll i = 0; i < n; i++)
edges.push_back({}), pref.push_back(0);
for (ll i = 0; i < n; i++)
{
scanf("%lld", &pref[i]);
prefs[pref[i]].push_back(i);
}
for (ll i = 1; i < n; i++)
{
ll temp;
scanf("%lld", &temp);
edges[temp].push_back(i);
}
dfs(0, 0);
for (ll p = 0; p < k; p++)
{
if (prefs[p].size() > 400)
dfs2(0, p);
else
{
consider.clear();
unordered_set<ll> temps;
temps.reserve(1 << 18);
temps.max_load_factor(0.25);
for (auto &i : prefs[p])
temps.insert(depth[i]);
for (auto &i : temps)
consider.push_back(i);
for (auto &i : prefs[p])
solve(i);
}
}
printf("%lld %lld\n", ans, ans2);
}
