#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pr;
const double pi=acos(-1);
#define rep(i,a,n) for(int i=a;i<=n;i++)
#define per(i,n,a) for(int i=n;i>=a;i--)
#define Rep(i,u) for(int i=head[u];i;i=Next[i])
#define clr(a) memset(a,0,sizeof a)
#define pb push_back
#define mp make_pair
#define fi first
#define sc second
ld eps=1e-9;
ll pp=1000000007;
ll mo(ll a,ll pp){if(a>=0 && a<pp)return a;a%=pp;if(a<0)a+=pp;return a;}
ll powmod(ll a,ll b,ll pp){ll ans=1;for(;b;b>>=1,a=mo(a*a,pp))if(b&1)ans=mo(ans*a,pp);return ans;}
ll read(){
    ll ans=0;
    char last=' ',ch=getchar();
    while(ch<'0' || ch>'9')last=ch,ch=getchar();
    while(ch>='0' && ch<='9')ans=ans*10+ch-'0',ch=getchar();
    if(last=='-')ans=-ans;
    return ans;
}
//head
#define N 60001
int Min[N],dep[N],fa[N][20],v[N],Next[N],head[N],sum[N],num=0,cost[N],n;
int pre[N][20],Max[N];
void add(int x,int y){
    v[++num]=y;Next[num]=head[x];head[x]=num;
}
void dfs1(int u){
    pre[u][0]=cost[u];
    for(int i=1;(1<<i)<=dep[u];i++){
        fa[u][i]=fa[fa[u][i-1]][i-1];
        pre[u][i]=max(pre[u][i-1],pre[fa[u][i-1]][i-1]);
        }
    if(head[u])Min[u]=1000000000;
    else Min[u]=cost[u],Max[u]=cost[u];
    sum[u]+=cost[u];
    for(int i=head[u];i;i=Next[i]){
        sum[v[i]]=sum[u];
        dep[v[i]]=dep[u]+1;
        dfs1(v[i]);
        if(Min[v[i]]+cost[u]<Min[u] || Min[v[i]]+cost[u]==Min[u] && max(Max[v[i]],cost[u])>Max[u]){
            Min[u]=Min[v[i]]+cost[u];
            Max[u]=max(Max[v[i]],cost[u]);
            }
    }
}
void dfs2(int u){
    for(int i=head[u];i;i=Next[i]){
        if(Min[u]+cost[v[i]]<Min[v[i]] || Min[u]+cost[v[i]]==Min[v[i]] && max(Max[u],cost[v[i]])>Max[v[i]]){
            Min[v[i]]=Min[u]+cost[v[i]];
            Max[v[i]]=max(Max[u],cost[v[i]]);
            }
        dfs2(v[i]);
    }
}
int lca(int x,int y){
    if(dep[x]<dep[y])swap(x,y);
    for(int i=16;i>=0;i--)
        if(dep[x]-(1<<i)>=dep[y])x=fa[x][i];
    if(x==y)return x;
    for(int i=16;i>=0;i--)
        if(dep[x]>=(1<<i) && fa[x][i]!=fa[y][i]){
            x=fa[x][i];
            y=fa[y][i];
        }
    return fa[x][0];
}
int get(int x,int y){
    int ans=cost[y];
    for(int i=16;i>=0;i--)
        if(dep[x]-(1<<i)>=dep[y]){
            ans=max(ans,pre[x][i]);
            x=fa[x][i];
        }
    return ans;
}
int main(){
    int T=read();
    while(T--){
        memset(sum,0,sizeof sum);
        memset(dep,0,sizeof dep);
        memset(pre,0,sizeof pre);
        n=read();
        num=0;
        rep(i,1,n)head[i]=0;
        int Q=read();
        rep(i,2,n){
            fa[i][0]=read();
            add(fa[i][0],i);
            }
        rep(i,1,n)cost[i]=read();
        dfs1(1);
        dfs2(1);
        rep(i,1,n){
            int s1=Min[i]+cost[1],t1=max(Max[i],cost[1]);
            int s2=sum[i],t2=get(i,1);
            if(s1<s2 || s1==s2 && t1>t2)Min[i]=s1,Max[i]=t1;
            else Min[i]=s2,Max[i]=t2;
        }
        while(Q--){
            int x=read(),y=read();
            int z=lca(x,y);
            int ans1=sum[x]+sum[y]-sum[z]-sum[fa[z][0]],t1=max(get(x,z),get(y,z));
            int ans2=Min[x]+Min[y]-cost[1],t2=max(Max[x],Max[y]);
            if(ans1<ans2 || ans1==ans2 && t1>t2)printf("%d %d\n",ans1,t1);
            else printf("%d %d\n",ans2,t2);
        }
    }
    return 0;
}