#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define int long long
#define maxn 100005
#define mi LLONG_MIN
#define ma LLONG_MAX
#define mod 1000000007
#define pb push_back
#define S second
#define F first
int n, q;
const int K = 18;
int up[K][maxn], d[maxn];
struct mat
{
int m[5][5];
mat()
{
for (int i = 0; i < 5; i++)
{
for (int j = 0; j < 5; j++)
{
m[i][j] = -1e18;
}
}
}
};
mat merge(mat a, mat b)
{
mat c;
for (int i = 0; i < 5; i++)
{
for (int j = 0; j < 5; j++)
{
for (int k = 0; k < 5; k++)
{
if (a.m[i][k] <= -1e16 || b.m[k][j] <= -1e16)
continue;
c.m[i][j] = max(c.m[i][j], a.m[i][k] + b.m[k][j]);
}
}
}
return c;
}
mat mup[K][maxn], mdown[K][maxn];
vector<int> g[maxn], r(maxn), b(maxn);
void dfs(int u = 0, int p = 0, int dep = 0)
{
stack<int> st;
st.push(u);
d[u] = dep;
up[0][u] = p;
mat matr;
matr.m[1][0] = r[u];
matr.m[2][1] = r[u];
matr.m[0][1] = b[u];
matr.m[1][2] = b[u];
matr.m[3][2] = r[u];
matr.m[2][3] = b[u];
matr.m[4][3] = r[u];
matr.m[3][4] = b[u];
mup[0][u] = matr;
mdown[0][u] = matr;
while (!st.empty())
{
int v = st.top();
st.pop();
for (int it : g[v])
{
if (it == up[0][v])
continue;
up[0][it] = v;
d[it] = d[v] + 1;
mat matre;
matre.m[1][0] = r[it];
matre.m[2][1] = r[it];
matre.m[0][1] = b[it];
matre.m[1][2] = b[it];
matre.m[3][2] = r[it];
matre.m[2][3] = b[it];
matre.m[4][3] = r[it];
matre.m[3][4] = b[it];
mup[0][it] = matre;
mdown[0][it] = matre;
st.push(it);
}
}
}
int get(int u, int v)
{
if (d[u] < d[v])
swap(u, v);
for (int i = K - 1; i >= 0; i--)
{
if (d[u] - (1 << i) >= d[v])
u = up[i][u];
}
if (u == v)
return u;
for (int i = K - 1; i >= 0; i--)
{
if (up[i][u] != up[i][v])
{
u = up[i][u];
v = up[i][v];
}
}
return up[0][u];
}
int32_t main()
{
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin >> n >> q;
for (int i = 0; i < n; i++)
{
cin >> b[i];
}
for (int i = 0; i < n; i++)
{
cin >> r[i];
}
for (int i = 0; i < n - 1; i++)
{
int u, v;
cin >> u >> v;
u--;
v--;
g[u].pb(v);
g[v].pb(u);
}
dfs();
for (int i = 1; i < K; i++)
{
for (int j = 0; j < n; j++)
{
up[i][j] = up[i - 1][up[i - 1][j]];
mup[i][j] = merge(mup[i - 1][j], mup[i - 1][up[i - 1][j]]);
mdown[i][j] = merge(mdown[i - 1][up[i - 1][j]], mdown[i - 1][j]);
}
}
while (q--)
{
int u, v;
cin >> u >> v;
u--;
v--;
int lca = get(u, v);
mat U;
for (int i = 0; i < 5; i++)
U.m[i][i] = 0;
int c = u;
for (int i = K - 1; i >= 0; i--)
{
if (d[c] - (1 << i) >= d[lca])
{
U = merge(U, mup[i][c]);
c = up[i][c];
}
}
mat V;
for (int i = 0; i < 5; i++)
V.m[i][i] = 0;
c = v;
for (int i = K - 1; i >= 0; i--)
{
if (d[c] - (1 << i) >= d[lca])
{
V = merge(mdown[i][c], V);
c = up[i][c];
}
}
mat lca_mat = mup[0][lca];
mat an = merge(U, merge(lca_mat, V));
int ans = mi;
for (int i = 0; i < 5; i++)
{
ans = max(ans, an.m[2][i]);
}
cout << ans << endl;
}
}
