#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
#define PB push_back
const ll INF = (ll)1e18 + 7;
const int logo = 17;
const int MAXN = 1e5 + 7;
struct mat{
ll a[5][5];
mat(){
for(int i=0; i<5; i++){
for(int j=0; j<5; j++) a[i][j] = -INF;
}
}
void res(){
for(int i=0; i<5; i++){
for(int j=0; j<5; j++) a[i][j] = -INF;
}
}
};
int par[logo][MAXN], dep[MAXN], vl[2][MAXN];
mat f[logo][MAXN], f2[logo][MAXN], res, res2;
vi g[MAXN];
void mrg(mat &c, mat a, mat b){
c.res();
for(int i=0; i<5; i++){
for(int j=0; j<5; j++){
for(int k=0; k<5; k++){
c.a[i][j] = max(c.a[i][j], a.a[i][k] + b.a[k][j]);
}
}
}
}
void dfs(int u, int p = -1){
if(p == -1){
dep[u] = 1;
par[0][u] = u;
}else{
dep[u] = dep[p] + 1;
par[0][u] = p;
}
for(auto &x : g[u]) if(x != p) dfs(x, u);
}
int getLCA(int a, int b){
if(dep[a] < dep[b]) swap(a, b);
int delta = dep[a] - dep[b];
for(int i = 0; i < logo; i++) if(delta & (1 << i)) a = par[i][a];
if(a == b) return a;
for(int i = logo - 1; i >= 0; i--){
if(par[i][a] != par[i][b]){
a = par[i][a], b = par[i][b];
}
}
return par[0][a];
}
void solve(){
int n, q;
cin >> n >> q;
for(int i = 1; i <= n; i++) cin >> vl[0][i];
for(int i = 1; i <= n; i++) cin >> vl[1][i];
for(int i = 1, a, b; i < n; i++){
cin >> a >> b;
g[a].PB(b);
g[b].PB(a);
}
g[0].PB(1);
dfs(0);
for(int i = 0; i <= n; i++){
for(int fir = 0; fir < 4; fir++) f[0][i].a[fir][fir + 1] = vl[0][i];
for(int fir = 1; fir < 5; fir++) f[0][i].a[fir][fir - 1] = vl[1][i];
f2[0][i] = f[0][i];
}
for(int j = 1; j < logo; j++){
for(int i = 0; i <= n; i++){
int nex = par[j - 1][i];
par[j][i] = par[j - 1][nex];
mrg(f[j][i], f[j - 1][i], f[j - 1][nex]);
mrg(f2[j][i], f2[j - 1][nex], f2[j - 1][i]);
}
}
while(q--){
int a, b, c;
cin >> a >> b;
c = getLCA(a, b);
res.res();
res.a[2][2] = 0;
int delta = dep[a] - dep[c];
for(int i = logo - 1; i >= 0; i--){
if(!(delta & (1 << i))) continue;
mrg(res, res, f[i][a]);
a = par[i][a];
}
mrg(res, res, f[0][c]);
bool fir = 1;
delta = dep[b] - dep[c];
for(int i = logo - 1; i >= 0; i--){
if(!(delta & (1 << i))) continue;
if(fir) res2 = f2[i][b];
else mrg(res2, f2[i][b], res2);
b = par[i][b];
fir = 0;
}
if(delta) mrg(res, res, res2);
ll ans = -INF;
for(int i=0; i<5; i++) ans = max(ans, res.a[2][i]);
cout << ans << "\n";
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
solve();
return 0;
}
