#include <bits/stdc++.h>
#define fst first
#define snd second
#define pb push_back
#define SZ(x) (int)x.size()
#define ALL(x) x.begin(),x.end()
#define forn(i,a,b) for(int i = a; i<b; i++)
#define mset(a,v) memset(a,v,sizeof(a))
#define FIN ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using namespace std;
typedef long long ll;
const int MAXN = 200000+5;
ll n,q;
ll red[MAXN];
ll blue[MAXN];
bool vis[MAXN];
bool block[MAXN];
ll cnt[MAXN];
vector<ll> adj[MAXN];
ll Find(ll nd, ll p, ll ori){
for(auto i:adj[nd]) if(i!=p && !block[i]){
if(cnt[i]*2>cnt[ori]){
return Find(i,nd,ori);
}
}
return nd;
}
void dfs(ll nd, ll p){
vis[nd]=true;
if(block[nd]) return;
cnt[nd]=1;
for(auto i:adj[nd]) if(i!=p){
dfs(i,nd);
cnt[nd]+=cnt[i];
}
}
ll myround[MAXN];
ll dp[MAXN][10];
ll cen;
// diferencia red-blue
/*
0=-2
1=-1
2=0
3=1
4=2
*/
vector<ll> dif = {-2,-1,0,1,2};
void expand(ll nd, ll p, ll round){
//cout<<"expand to "<<nd<<'\n';
myround[nd]=round;
forn(t, 0, 5){
if(t-1>=0) dp[nd][t]=max( dp[nd][t] , dp[p][t-1]+red[nd] );
if(t+1<5) dp[nd][t]=max( dp[nd][t] , dp[p][t+1]+blue[nd] );
//cout<<"dp "<<t<<" "<<dp[nd][t]<<'\n';
}
for(auto i:adj[nd]) if(i!=p && !block[i]){
expand(i,nd,round);
}
}
bool centroid(){
mset(vis,false);
ll nd = -1;
forn(i,0,n) if(!vis[i] && !block[i]){
nd=i;
break;
}
if(nd==-1) return false;
dfs(nd,-1);
cen = Find(nd,-1,nd);
block[cen]=true;
mset(myround,-1);
forn(i,0,MAXN) forn(j,0,5){
dp[i][j]=-900000000000000000;
}
dp[cen][2]=0;
ll aux = 0;
for(auto i:adj[cen]) if(!block[i]){
expand(i,cen,aux);
aux++;
}
myround[cen]=aux+1;
//cout<<"Nuevo centroide : "<<cen<<"\n";
return true;
}
int main(){
cin>>n>>q;
forn(i,0,n) cin>>red[i];
forn(i,0,n) cin>>blue[i];
ll u,v;
forn(i,0,n-1){
cin>>u>>v; u--; v--;
adj[u].pb(v);
adj[v].pb(u);
}
vector<pair<ll,ll>> qu(q);
forn(i,0,q) cin>>qu[i].fst>>qu[i].snd , qu[i].fst--,qu[i].snd--;
vector<ll> res(q,-900000000000000000);
while(centroid()){
forn(i,0,q) if(qu[i].fst!=-1){
u=qu[i].fst;
v=qu[i].snd;
if(u==v){
qu[i].fst=-1;
res[i]=max(res[i],max(red[u],blue[u]));
}
if(myround[v]!=-1 && myround[u]!=-1 && myround[u]!=myround[v]){
forn(tu,0,5){
forn(tv,0,5){
ll rdif = dif[tu]+dif[tv];
if(rdif+1<=3){
/*cout<<u<<" "<<tu<<" = "<<dp[u][tu]<<'\n';
cout<<v<<" "<<tv<<" = "<<dp[v][tv]<<'\n';
cout<<"agrega red "<<red[cen]<<'\n';*/
res[i]=max(res[i], dp[u][tu]+dp[v][tv]+red[cen]);
}
if(rdif-1<=3){
/*cout<<u<<" "<<tu<<" = "<<dp[u][tu]<<'\n';
cout<<v<<" "<<tv<<" = "<<dp[v][tv]<<'\n';
cout<<"agrega blue "<<blue[cen]<<'\n';*/
res[i]=max(res[i], dp[u][tu]+dp[v][tv]+blue[cen]);
}
}
}
//cout<<"Se responde querie "<<i<<'\n';
qu[i].fst=-1;
}
}
}
for(auto i:res) cout<<i<<'\n';
return 0;
}
