#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;
#ifdef D
#define debug(x) cout << x
#else
#define debug(x) //nothing
#endif
const int MAXN = 200000+5;
ll n,q;
pair<ll,ll> qu[MAXN];
ll res[MAXN];
ll red[MAXN];
ll blue[MAXN];
ll subsz[MAXN];
ll isrem[MAXN];
vector<ll> adj[MAXN];
ll subtree_sz(ll nd, ll p){
//cout<<nd<<" "<<p<<'\n';
subsz[nd]=1;
for(auto i:adj[nd]) if(i!=p && !isrem[i]){
subsz[nd]+=subtree_sz(i,nd);
}
return subsz[nd];
}
ll get_centroid(ll nd , ll p, ll sztotal){
//cout<<nd<<" "<<p<<'\n';
for(auto i:adj[nd]) if(i!=p && !isrem[i]){
if(subsz[i]*2>sztotal) return get_centroid(i,nd,sztotal);
}
return nd;
}
/////////////////////
const int MAXS = 5;
#define INF ((ll)99999999999999999)
ll dp1[MAXN][MAXS][MAXS][MAXS];
//ll dp2[MAXN][MAXS][MAXS];
ll myp[MAXN];
ll myr[MAXN];
ll state[MAXN];
ll actualstate;
queue<ll> cola;
set<pair<ll,ll>> querie[MAXN];
void dfs(ll nd, ll p, ll centroid, ll round){
myp[nd]=p;
myr[nd]=round;
//cout<<nd<<" tam "<<SZ(querie[nd])<<'\n';
if(SZ(querie[nd])>0) cola.push(nd);
state[nd]=actualstate;
forn(i,0,5) forn(j,0,5) dp1[nd][i][j][0]=dp1[nd][i][j][1]=-INF;
ll aux = 1;
for(auto i:adj[nd]) if(i!=p && !isrem[i]){
if(nd==centroid) dfs(i,nd,centroid,round+aux), aux++;
else{
dfs(i,nd,centroid,round);
}
}
}
ll f1(ll x, ll y, ll z,ll type, ll centroid){
ll &res= dp1[x][y][z][type];
if(res!=-INF) return res;
if(type==0){
if(x==centroid && y==z) return 0;
if(x==centroid) return -INF;
}else{
if(x==centroid){
res=-INF;
if(y-1>=0 && y-1==z) res = max( res , red[x]);
if(y+1<5 && y+1==z) res= max( res, blue[x]);
return res;
}
}
res = -INF;
if(type==0){
if(y+1<5) res = max(res, f1(myp[x],y+1,z,type,centroid)+red[x]);
if(y-1>=0) res= max(res, f1(myp[x],y-1,z,type,centroid)+blue[x]);
}else{
if(y+1<5) res = max(res, f1(myp[x],y+1,z,type,centroid)+blue[x]);
if(y-1>=0) res= max(res, f1(myp[x],y-1,z,type,centroid)+red[x]);
}
return res;
}
////////////////////
void centroid_decomp(ll nd = 0){
ll centroid = get_centroid(nd,-1,subtree_sz(nd,-1));
isrem[centroid]=true;
///////////////
debug("New Centroid: "<<centroid<<'\n');
actualstate++;
//mset(myp,-1);
//mset(myr,-1);
while(!cola.empty()) cola.pop();
dfs(centroid,-1,centroid,0);
/*forn(i,0,n) if(myp[i]!=-1){
forn(j,0,5){
forn(k,0,5){
f1(i,j,k,centroid);
}
}
}*/
//forn(i,0,n) forn(j,0,5) forn(k,0,5) dp1[i][j][k][1]=dp1[i][j][k][0]=-INF;
while(!cola.empty()){
ll a = cola.front();
cola.pop();
debug("New nd "<<a<<'\n');
queue<pair<ll,pair<ll,ll>>> toerase;
for(auto B:querie[a]) if(res[B.snd]==-INF){
ll i = B.snd;
ll b = B.fst;
debug("- "<<b<<" "<<i<<'\n');
ll best = -INF;
//cout<<" "<<myr[a]<<" "<<myr[b]<<'\n';
if(myr[a]!=myr[b] && state[a]==actualstate && state[b]==actualstate){
forn(j,0,5){
forn(k,0,5){
debug("Probando "<<a<<" "<<2<<" "<<k<<" = "<<f1(a,2,k,0,centroid)<<" y "<<b<<" "<<j<<" "<<k<<" = "<<f1(b,j,k,1,centroid)<<'\n');
best=max(best,f1(a,2,k,0,centroid)+f1(b,j,k,1,centroid));
}
}
res[i]=best;
toerase.push({a,B});
}
//toerase.push({b,{a,i}});
}
while(!toerase.empty()){
ll c1 = toerase.front().fst; toerase.pop();
pair<ll,ll> pp = toerase.front().snd;
auto it = querie[c1].find(pp);
if(it!=querie[c1].end()) querie[c1].erase(it);
}
}
/*
forn(i,0,q) if(res[i]==-INF){
ll a = qu[i].fst;
ll b = qu[i].snd;
ll best = -INF;
//cout<<" "<<myr[a]<<" "<<myr[b]<<'\n';
if(myr[a]!=myr[b] && state[a]==actualstate && state[b]==actualstate){
forn(j,0,5){
forn(k,0,5){
debug("Probando "<<a<<" "<<2<<" "<<k<<" = "<<f1(a,2,k,0,centroid)<<" y "<<b<<" "<<j<<" "<<k<<" = "<<f1(b,j,k,1,centroid)<<'\n');
best=max(best,f1(a,2,k,0,centroid)+f1(b,j,k,1,centroid));
}
}
}
res[i]=best;
}*/
///////////////
for(auto i:adj[centroid]) if(!isrem[i]){
centroid_decomp(i);
}
}
int main(){ FIN;
mset(state,-1);
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);
}
forn(i,0,q){
cin>>qu[i].fst>>qu[i].snd; qu[i].fst--; qu[i].snd--;
res[i]=-INF;
if(qu[i].fst==qu[i].snd) res[i]=max(red[qu[i].fst], blue[qu[i].snd]);
else{
querie[qu[i].fst].insert({qu[i].snd,i});
//querie[qu[i].snd].insert({qu[i].fst,i});
}
}
centroid_decomp();
forn(i,0,q) cout<<res[i]<<'\n';
return 0;
}
