#include<bits/stdc++.h>
using namespace std;
//#define int long long
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef double db;
#define F(i, a, b) for(int i = a; i <= (b); ++i)
#define F2(i, a, b) for(int i = a; i < (b); ++i)
#define dF(i, a, b) for(int i = a; i >= (b); --i)
template<typename T> void debug(string s, T x) {cerr << "[" << s << "] = [" << x << "]\n";}
template<typename T, typename... Args> void debug(string s, T x, Args... args) {for (int i = 0, b = 0; i < (int)s.size(); i++) if (s[i] == '(' || s[i] == '{') b++;else if (s[i] == ')' || s[i] == '}') b--;else if (s[i] == ',' && b == 0) {cerr << "[" << s.substr(0, i) << "] = [" << x << "] | ";debug(s.substr(s.find_first_not_of(' ', i + 1)), args...);break;}}
#ifdef ONLINE_JUDGE
#define Debug(...)
#else
#define Debug(...) debug(#__VA_ARGS__, __VA_ARGS__)
#endif
#define pb push_back
#define fi first
#define se second
#define Mry fprintf(stderr, "%.3lf MB\n", (&Med - &Mbe) / 1048576.0)
#define Try cerr << 1e3 * clock() / CLOCKS_PER_SEC << " ms\n";
typedef long long ll;
// namespace Fread {const int SIZE = 1 << 17; char buf[SIZE], *S, *T; inline char getchar() {if (S == T) {T = (S = buf) + fread(buf, 1, SIZE, stdin); if (S == T) return '\n';} return *S++;}}
// namespace Fwrite {const int SIZE = 1 << 17; char buf[SIZE], *S = buf, *T = buf + SIZE; inline void flush() {fwrite(buf, 1, S - buf, stdout), S = buf;} inline void putchar(char c) {*S++ = c;if (S == T) flush();} struct NTR {~NTR() {flush();}} ztr;}
// #ifdef ONLINE_JUDGE
// #define getchar Fread::getchar
// #define putchar Fwrite::putchar
// #endif
inline int ri() {
int x = 0;
bool t = 0;
char c = getchar();
while (c < '0' || c > '9') t |= c == '-', c = getchar();
while (c >= '0' && c <= '9') x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
return t ? -x : x;
}
inline void wi(int x) {
if (x < 0) {
putchar('-'), x = -x;
}
if (x > 9) wi(x / 10);
putchar(x % 10 + 48);
}
inline void wi(int x, char s) {
wi(x), putchar(s);
}
bool Mbe;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
const int mod = 998244353;
const ll inf = 0x3f3f3f3f3f3f3f3f;
const int _ = 2e5 + 5;
bool Med;
int n, tot, head[_], to[_ << 1], nxt[_ << 1], w[_ << 1];
void add(int u, int v, int c) {
to[++tot] = v, nxt[tot] = head[u], head[u] = tot, w[tot] = c;
}
namespace Dis {
int dfn[_], cnt, Fa[_], st[_][20];
ll dep[_];
void dfs(int u, int fa) {
dfn[u] = ++cnt;
Fa[u] = fa;
st[dfn[u]][0] = u;
for(int i = head[u], v = to[i]; i; i = nxt[i], v = to[i]) if(v != fa) {
dep[v] = dep[u] + w[i];
dfs(v, u);
}
}
int get(int x, int y) {
return dfn[Fa[x]] < dfn[Fa[y]] ? x : y;
}
int lg[_];
int LCA(int u, int v) {
if(u == v) return u;
u = dfn[u], v = dfn[v];
if(u > v) swap(u, v);
u++;
int t = lg[v - u + 1];
return Fa[get(st[u][t], st[v - (1 << t) + 1][t])];
}
ll Dis(int u, int v) {
// Debug(u, v, LCA(u, v));
return dep[u] + dep[v] - (dep[LCA(u, v)] << 1);
}
void init() {
F(i, 2, n) lg[i] = lg[i >> 1] + 1;
dfs(1, 0);
F(j, 1, lg[n]) {
F(i, 1, n - (1 << j) + 1) st[i][j] = get(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
}
}
}
ll f[_];
int Sum, rt, sz[_]; bool vis[_];
void get_rt(int u, int fa) {
int mx = 0;
for(int i = head[u], v = to[i]; i; i = nxt[i], v = to[i]) if(v != fa &&!vis[v]) {
get_rt(v, u);
mx = max(mx, sz[v]);
}
mx = max(mx, Sum - sz[u]);
if(mx <= Sum / 2) {
rt = u;
}
}
void get_sz(int u, int fa) {
sz[u] = 1;
for(int i = head[u], v = to[i]; i; i = nxt[i], v = to[i]) if(v != fa && !vis[v]) {
get_sz(v, u);
sz[u] += sz[v];
}
}
int Fa[_];
void work(int u) {
// Debug(u);
vis[u] = 1;
for(int i = head[u], v = to[i]; i; i = nxt[i], v = to[i]) if(!vis[v]) {
get_sz(v, u);
Sum = sz[v];
get_rt(v, u);
Fa[rt] = u;
work(rt);
}
}
pair<ll, ll> operator - (pair<ll, ll> a, pair<ll, ll> b) {
return make_pair(a.fi - b.fi, a.se - b.se);
}
struct Tubao {
vector<pair<ll, ll>> a;
void ins(ll x, ll y) {
if(a.empty()) {
a.pb({x, y});
return;
}
while(a.size() > 1 && 1ll * (a.back().se - a[(int)a.size() - 2].se) * (x - a.back().fi) < 1ll * (a.back().fi - a[(int)a.size() - 2].fi) * (y - a.back().se)) a.pop_back();
a.pb({x, y});
}
ll qry(ll x) {
if(a.empty()) {
return inf;
}
// ll res = inf;
// for(pair<ll, ll> v : a) res = min(res, v.fi * x + v.se);
// return res;
if((int)a.size() == 1) {
return a.front().fi * x + a.front().se;
}
int l = 1, r = (int)a.size() - 1, mid, res = 0;
while(l <= r) {
mid = (l + r) >> 1;
if((a[mid].se - a[mid - 1].se) <= (a[mid].fi - a[mid - 1].fi) * (-x)) {
l = mid + 1;
res = mid;
} else {
r = mid - 1;
}
}
return a[res].fi * x + a[res].se;
}
} d[_];
ll a[_], b[_];
void ins(int u) {
for(int nw = u; nw; nw = Fa[nw]) {
d[nw].ins(a[u], f[u] + a[u] * Dis::Dis(u, nw) + b[u]);
}
}
ll qry(int u) {
ll res = inf;
for(int nw = u; nw; nw = Fa[nw]) {
res = min(res, d[nw].qry(Dis::Dis(u, nw)));
}
return res;
}
int p[_];
vector<long long> travel(vector<long long> A, vector<int> B, vector<int> U, vector<int> V, vector<int> W) {
n = A.size();
F(i, 1, n) a[i] = B[i - 1], b[i] = A[i - 1];
F(i, 0, n - 2) {
U[i]++, V[i]++;
add(U[i], V[i], W[i]);
add(V[i], U[i], W[i]);
}
Dis::init();
// Debug("Yes");
f[1] = 0;
F(i, 2, n) f[i] = a[1] * Dis::Dis(1, i) + b[1];
// Debug("2");
Sum = n;
get_sz(1, 0);
get_rt(1, 0);
work(rt);
// Debug("done");
F(i, 1, n) p[i] = i;
sort(p + 1, p + n + 1, [&](int a1, int b1) { return a[a1] > a[b1]; });
ins(1);
// F(i, 2, n) Debug(i, f[i], Dis::Dis(1, i));
F(i, 1, n) {
if(p[i] == 1) continue;
// Debug(p[i], f[p[i]], qry(p[i]));
f[p[i]] = qry(p[i]);
ins(p[i]);
// Debug(qry(p[i]));
}
F(i, 1, n) {
Debug(i, qry(i));
}
vector<ll> f2;
F(i, 2, n) f2.pb(qry(i));
return f2;
}
signed main() {
// Mry;
travel({10, 5, 13, 4, 3}, {10, 7, 5, 9, 1}, {1, 0, 3, 2}, {0, 2, 2, 4}, {1, 5, 10, 3});
// Try;
return 0;
}