#include <bits/stdc++.h>
// #include "../cpp-dump/cpp-dump.hpp"
template<class T>
void chkmin(T &x, const T &y) {
  if (x > y) x = y;
} 
using ll = long long;

struct sgt {
  struct line { 
    ll k, b;
    ll eval(ll x) { return k * x + b; }
  };
  static int const BUF = 2e6;
  static line tr[BUF];
  static int ls[BUF], rs[BUF], ntot;

  int rt;
  ll l, r;
  void insert(int &i, ll l, ll r, line li) {
    if (!i) return tr[i = ++ntot] = li, void();
    auto mid = (l + r) >> 1;
    if (li.eval(mid) < tr[i].eval(mid)) std::swap(li, tr[i]);
    if (li.eval(l) < tr[i].eval(l)) insert(ls[i], l, mid, li);
    if (li.eval(r) < tr[i].eval(r)) insert(rs[i], mid + 1, r, li);
  }
  ll query(int i, ll l, ll r, ll p) {
    if (!i) return 1e18;
    auto mid = (l + r) >> 1;
    if (p <= mid) return std::min(query(ls[i], l, mid, p), tr[i].eval(p));
    else return std::min(query(rs[i], mid + 1, r, p), tr[i].eval(p));
  }
  sgt(ll l, ll r) : rt(0), l(l), r(r) {}
  void insert(line li) { insert(rt, l, r, li); }
  auto query(ll p) { return query(rt, l, r, p); }  
};

sgt::line sgt::tr[sgt::BUF];
int sgt::ls[sgt::BUF], sgt::rs[sgt::BUF], sgt::ntot;

std::vector<ll> travel(std::vector<ll> a, std::vector<int> b,
                       std::vector<int> u, std::vector<int> v,
                       std::vector<int> w) {
  int n = a.size();
  a.insert(a.begin(), 0), b.insert(b.begin(), 0);
  std::vector<std::vector<std::pair<int, int>>> g(n + 1);
  for (int i = 0; i < n - 1; i++) {
    ++u[i], ++v[i];
    g[u[i]].emplace_back(v[i], w[i]);
    g[v[i]].emplace_back(u[i], w[i]);
  }
  std::vector<std::vector<std::pair<int, ll>>> h(n + 1);
  std::vector<int> vis(n + 1);
  auto build = [&](auto &self, int u) -> void {
    int tot = 0;
    auto dfs1 = [&](auto &self, int u, int ff) -> void {
      tot += 1;
      for (auto [v, w] : g[u])
        if (v != ff && !vis[v]) self(self, v, u);
    };
    int rt = 0;
    auto dfs2 = [&](auto &self, int u, int ff) -> int {
      int ret = 1;
      for (auto [v, w] : g[u])
        if (v != ff && !vis[v]) ret += self(self, v, u);
      if (ret * 2 >= tot && !rt) rt = u;
      return ret;
    };
    dfs1(dfs1, u, 0), dfs2(dfs2, u, 0);
    auto dfs3 = [&](auto &self, int u, int ff, ll d) -> void {
      h[u].emplace_back(rt, d);
      for (auto [v, w] : g[u])
        if (v != ff && !vis[v])
          self(self, v, u, d + w);
    };
    dfs3(dfs3, rt, 0, 0);
    vis[rt] = 1;
    for (auto [v, w] : g[rt])
      if (!vis[v])
        self(self, v);
  };
  build(build, 1);
  // cpp_dump(h);
  std::vector<sgt> tr(n + 1, sgt(0, 1e11));
  auto query = [&](int u) {
    ll ret = 1e18;
    for (auto [id, dis] : h[u])
      chkmin(ret, tr[id].query(dis));
    return ret;
  };
  auto update = [&](int u, ll d) {
    for (auto [id, dis] : h[u])
      tr[id].insert({b[u], a[u] + d + b[u] * dis});
  };
  std::vector<int> id(n - 1);
  std::iota(id.begin(), id.end(), 2);
  std::sort(id.begin(), id.end(), [&](int u, int v) { return b[u] < b[v]; });
  update(1, 0);
  for (int i : id) {
    auto d = query(i);
    update(i, d);
  }
  std::vector<ll> ret;
  for (int i = 2; i <= n; i++)
    ret.push_back(query(i));
  return ret;
}