#include <bits/stdc++.h>
using namespace std;
#define int long long
#define all(x) x.begin(), x.end()
#define chmax(v, x) v = max(v, x)
const int mxN = 1e5 + 5;
const int INF = -1e18;
const int mxB = 20;
const int K = 2;
int col[mxN][2];
vector<int> adj[mxN];
struct Mat{
array<array<int, 5>, 5> dp;
Mat(){
for(int i = 0; i < 5; ++i){
for(int j = 0; j < 5; ++j){
dp[i][j] = 0;
}
}
}
static Mat inf(){
Mat m = Mat();
for(int i = 0; i < 5; ++i){
for(int j = 0; j < 5; ++j){
m.dp[i][j] = INF;
}
}
return m;
}
Mat merge(Mat &other){
Mat nw = inf();
for(int st = -2; st <= 2; ++st){
for(int en = -2; en <= 2; ++en){
for(int nen = -2; nen <= 2; ++nen){
chmax(nw.dp[st + K][nen + K], dp[st + K][en + K] + other.dp[en + K][nen + K]);
}
}
}
return nw;
}
};
Mat up[mxN][mxB], down[mxN][mxB], cur[mxN];
int tp[mxN][mxB], dep[mxN];
void dfs(int u = 1, int par = 0){
cur[u] = Mat::inf();
for(int st = -2; st <= 1; ++st){
cur[u].dp[st + K][st + 1 + K] = col[u][0];
}
for(int st = -1; st <= 2; ++st){
cur[u].dp[st + K][st - 1 + K] = col[u][1];
}
tp[u][0] = par, up[u][0] = cur[par];
down[u][0] = cur[u], dep[u] = dep[par] + 1;
for(int j = 1; j < mxB; ++j){
int v = tp[u][j - 1];
tp[u][j] = tp[v][j - 1];
up[u][j] = up[u][j - 1].merge(up[v][j - 1]);
down[u][j] = down[v][j - 1].merge(down[u][j - 1]);
}
for(auto it : adj[u]){
if(it ^ par) dfs(it, u);
}
}
int kth(int u, int k){
for(int i = mxB - 1; i >= 0; --i){
if(k & (1 << i)) u = tp[u][i];
}
return u;
}
int lca(int u, int v){
if(dep[u] < dep[v]) swap(u, v);
u = kth(u, dep[u] - dep[v]);
if(u == v) return u;
for(int j = mxB - 1; j >= 0; --j){
if(tp[u][j] ^ tp[v][j]) u = tp[u][j], v = tp[v][j];
}
return tp[u][0];
}
int query(int u, int v){
int l = lca(u, v);
Mat left = cur[u];
for (int j=0; j<mxB; j++) if ((dep[u] - dep[l])>>j&1) {
left = left.merge(up[u][j]);
u = tp[u][j];
}
Mat right = Mat();
for (int j=0; j<mxB; j++) if ((dep[v] - dep[l])>>j&1) {
right = down[v][j].merge(right);
v = tp[v][j];
}
Mat z = left.merge(right);
return *max_element(all(z.dp[2]));
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(nullptr); cout.tie(nullptr);
int n, q;
cin >> n >> q;
for(int i = 1; i <= n; ++i){
cin >> col[i][0];
}
for(int i = 1; i <= n; ++i){
cin >> col[i][1];
}
for(int i = 1, u, v; i <= n - 1; ++i){
cin >> u >> v;
adj[u].push_back(v);
adj[v].push_back(u);
}
dfs();
while(q--){
int u, v;
cin >> u >> v;
cout << query(u, v) << "\n";
}
return 0;
}
