#include<bits/stdc++.h>
using namespace std;
#define N 100005
#define B 350
#define pb push_back
int *f[N],ff[N<<1],*ch=ff,son[N],len[N];
int in[N],out[N],dep[N],col[N],tt,fl[N],n,k,ret[N],ret1[N],ct[N];
vector<int>rd[N],cl[N];int cl1[N];
bool cmp(int a,int b){return dep[a]>dep[b];}
void dfs(int u){
	in[u]=out[u]=++tt;
	son[u]=-1;len[u]=0;
	for(int v:rd[u]){
		dep[v]=dep[u]+1,dfs(v),out[u]=out[v];
		if(len[u]<len[v]+1)len[u]=len[v]+1,son[u]=v;
    }if(son[u]!=-1)fl[son[u]]=1;
}
void dfs1(int u){
	for(int v:rd[u]){if(v==son[u])f[v]=f[u]+1;dfs1(v);}++f[u][0];
	for(int v:rd[u]){
		if(v==son[u])continue;
		for(int j=0;j<=len[v];++j)f[u][j+1]+=f[v][j];
    }
    if(cl1[col[u]]<=B){
    	for(int v:cl[col[u]]){
    		if(in[v]>=in[u]&&in[v]<=out[u])++ret1[u];
    		if(dep[v]-dep[u]<=len[u])ret[u]+=(ct[dep[v]]<f[u][dep[v]-dep[u]]),++ct[dep[v]];
    		if(v==u)break;
		}
		for(int v:cl[col[u]]){ct[dep[v]]=0;if(v==u)break;}
	}
}
int ss[N],ss1[N],ct1[N];
void dfs2(int u,int cc){
	ss1[u]=(col[u]==cc),ss[u]=0;
	for(int v:rd[u])dfs2(v,cc),ss1[u]+=ss1[v];
	if(son[u]>0)ss[u]=ss[son[u]];
	ss[u]+=(f[u][0]+1<=ct1[dep[u]]);
	f[u][0]=min(ct1[dep[u]],f[u][0]+1);
	for(int v:rd[u]){
		if(v==son[u])continue;
		for(int j=0;j<=len[v];++j){
			ss[u]-=f[u][j+1];
			f[u][j+1]=min(f[u][j+1]+f[v][j],ct1[dep[u]+j+1]);
			ss[u]+=f[u][j+1];
		}
    }
	if(col[u]==cc)ret[u]=ss[u],ret1[u]=ss1[u];
}
int main(){
	ios::sync_with_stdio(0),cin>>n>>k;
	for(int i=1;i<=n;++i)cin>>col[i],++col[i],cl[col[i]].pb(i),++cl1[col[i]];
	for(int i=2,x;i<=n;++i)cin>>x,++x,rd[x].pb(i);dfs(1);
	for(int i=1;i<=n;++i)if(!fl[i])f[i]=ch,ch+=len[i]+1;
	for(int i=1;i<=k;++i)sort(cl[i].begin(),cl[i].end(),cmp);
	dfs1(1);
	for(int cc=1;cc<=k;++cc){
		if(cl1[cc]<=B)continue;
		for(int i=0;i<=n+1;++i)ff[i]=ct1[i]=0;
		for(int v:cl[cc])++ct1[dep[v]];
		dfs2(1,cc);
	}
	int mx=-1,mx1=0;
	for(int i=1;i<=n;++i){
		if(mx<ret[i])mx=ret[i],mx1=ret[i]-ret1[i];
		else if(mx==ret[i]&&mx1>ret[i]-ret1[i])mx1=ret[i]-ret1[i];
	}cout<<mx<<" "<<mx1;
	return 0;
}