#include"bits/stdc++.h"
#include"ext/pb_ds/tree_policy.hpp"
#include"ext/pb_ds/assoc_container.hpp"
using namespace std;
using namespace __gnu_pbds;
#define FOR(i,a,b)for(int i=a;i<b;i++)
#define F0R(i,a)FOR(i,0,a)
#define ROF(i,a,b)for(int i=b-1;a<=i;i--)
#define R0F(i,a)ROF(i,0,a)
#define rep(a)F0R(_,a)
#define each(a,x)for(auto&a:x)
#define all(a)begin(a),end(a)
#define sz(x)int(size(x))
#define lla(x)rbegin(x),rend(x)
#define SUM(a)accumulate(all(a),0ll)
#define SUMM(a,b)accumulate(a,a+b,0ll)
#define MAX(a)*max_element(all(a))
#define MAXX(a,b)*max_element(a,a+b)
#define MIN(a)*min_element(all(a))
#define MINN(a,b)*min_element(a,a+b)
#define con const int
#define lwb lower_bound
#define upb upper_bound
#define bry binary_search
#ifdef LOCAL
#define print(x)cout<<x;
#else
#define print(...)
#endif
#define debug(x)print(#x<<" = "<<x<<endl)
using ld=long double;
using ll=long long;
using str=string;
template<class T>using oset=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
template<class T>using omset=tree<T,null_type,less_equal<T>,rb_tree_tag,tree_order_statistics_node_update>;
template<class T>T minn(T a){return a;}
template<class T,class...Args>T minn(T a,Args... args){return min(a,minn(args...));}
template<class T>T maxx(T a){return a;}
template<class T,class...Args>T maxx(T a,Args... args){return max(a,maxx(args...));}
#define SMIN(a,b...)a=min(a,minn(b))
#define SMAX(a,b...)a=max(a,maxx(b))
void fileset(str a){assert(nullptr!=freopen((a+".in").c_str(),"r",stdin)&&nullptr!=freopen((a+".out").c_str(),"w",stdout));}
con mxN = 2e5 + 5;

map<int,int> cntDepth[mxN];

vector<int> teamies[mxN];
vector<int> aj[mxN];

int ent[mxN];
int ext[mxN];
int col[mxN];
int dep[mxN];

int ans = INT_MIN;
int bbl = INT_MAX;

int tr;

int isInside(int u, int v){
    return ent[u] <= ent[v] && ext[v] <= ext[u];
}

void preCalc(int u, int d){
    dep[u] = d, ent[u] = tr ++;

    each (v, aj[u]){
        preCalc(v, d + 1);
    }

    ext[u] = tr ++;
}

void solve(int u){
    cntDepth[u][dep[u]] = 1;

    each (v, aj[u]){
        solve(v);

        if (sz(cntDepth[v]) > sz(cntDepth[u])){
            swap(cntDepth[v], cntDepth[u]);
        }

        each (pr, cntDepth[v]){
            auto [depth, cnt] = pr;
            cntDepth[u][depth] += cnt;
        }
    }

    int loc = 1;
    int swp = 0;
    int cnt = 0;
    int und = 0;

    int n = sz(teamies[col[u]]);

    F0R (i, n){
        int v = teamies[col[u]][i];

        if (dep[u] ^ dep[v]){
            if (isInside(u, v)) loc ++, und ++;
            else cnt ++;

            if (i < n - 1 && dep[v] ^ dep[teamies[col[u]][i + 1]]){
                if (cntDepth[u].count(dep[v])){
                    int tmp = max(0, min(cnt, cntDepth[u][dep[v]] - und));
                    loc += tmp, swp += tmp;
                }

                cnt = 0;
            }
        } else {
            cnt = 0;
        }
    }

    if (loc > ans){
        ans = loc, bbl = swp;
    } else if (loc == ans){
        bbl = min(bbl, swp);
    }
}

int main(){
    int N, K;
    cin >> N >> K;

    F0R (i, N){
        cin >> col[i];
    }

    FOR (i, 1, N){
        int B;
        cin >> B;

        aj[B].push_back(i);
    }

    preCalc(0, 0);

    F0R (i, N){
        teamies[col[i]].push_back(i);
    }

    ent[N] = INT_MIN;
    ext[N] = INT_MAX;

    F0R (i, K){
        sort(all(teamies[i]),[](int i, int j){
            return dep[i] < dep[j];
        });
        teamies[col[i]].push_back(N);
    }

    solve(0);

    cout << ans << ' ' << bbl << endl;
}