#include<stdio.h>
#include<vector>
#include<algorithm>
#define M 100005
using namespace std;
int n;
long long a[M],W[M],F[M];
int b[M],st[M],tp;
struct Edge{
	int x,w;
	operator int() const{return x;}
};
vector<Edge> G[M];
struct Line{
	long long k,b;
	inline long long operator()(long long x) const{return k*x+b;}
};
struct SGT{
	struct Node{
		int ls,rs;Line s;
	} tr[M<<5];
	int tot;
	void upd(int &x,long long l,long long r,Line u){
		if(!x) return tr[x=++tot]={0,0,u},void();
		Line &v=tr[x].s;long long mid=l+r>>1;
		if(u(mid)<=v(mid)) swap(u,v);
		long long ul=u(l),ur=u(r),vl=v(l),vr=v(r);
		if(ul>=vl&&ur>=vr) return;
		if(ul<=vl&&ur<=vr) return tr[x].s=u,void();
		if(ul<=vl) upd(tr[x].ls,l,mid,u);
		if(ur<=vr) upd(tr[x].rs,mid+1,r,u);
	}
	long long que(int x,long long l,long long r,long long k){
		if(!x) return 0x7fffffffffffffff;
		long long res=tr[x].s(k);
		if(l==r) return res;
		long long mid=l+r>>1;
		if(k<=mid) res=min(res,que(tr[x].ls,l,mid,k));
		if(k>mid) res=min(res,que(tr[x].rs,mid+1,r,k));
		return res;
	}
} sgt;
int sz[M],dep[M],top[M],big[M],f[M],rt[M],fa[M];
void dfs(int x,int fa){
	sz[x]=1,dep[x]=dep[fa]+1,f[x]=fa;
	for(auto [p,w]:G[x]) if(p!=fa)
		W[p]=W[x]+w,dfs(p,x),
		sz[x]+=sz[p],(sz[p]>sz[big[x]])&&(big[x]=p);
}
void ctp(int x,int tp){
	top[x]=tp;
	if(big[x]) ctp(big[x],tp);
	for(int p:G[x]) if(p!=big[x]&&p!=f[x])
		ctp(p,p);
}
int LCA(int x,int y){
	while(top[x]!=top[y]){
		if(dep[top[x]]>dep[top[y]]) x=f[top[x]];
		else y=f[top[y]];
	}
	return dep[x]<dep[y]?x:y;
}
long long dis(int x,int y){return W[x]+W[y]-2*W[LCA(x,y)];}
namespace ASD{
int sz[M],all,mn,rt;
bool vis[M];
void frt(int x){
	sz[x]=1,vis[x]=1;
	int mx=0;
	for(int p:G[x]) if(!vis[p])
		frt(p),mx=max(mx,sz[p]),sz[x]+=sz[p];
	mx=max(mx,all-sz[x]);
	if(mx<mn) mn=mx,rt=x;
	vis[x]=0;
}
void dfs(int x){
	vis[x]=1,sz[x]=1;
	for(int p:G[x]) if(!vis[p])
		dfs(p),sz[x]+=sz[p];
	vis[x]=0;
}
int div(int x){
	mn=0x7fffffff,frt(x),x=rt,vis[x]=1;
	for(int p:G[x]) if(!vis[p])
		dfs(p),all=sz[p],fa[div(p)]=x;
	return x;
}
void work(){all=n,div(1);}
}
inline void cal(int x){
	for(int t=x;t;t=fa[t]) F[x]=min(F[x],sgt.que(rt[t],1,1e11,dis(x,t)));
}
inline void ins(int x){
	for(int t=x;t;t=fa[t]) sgt.upd(rt[t],1,1e11,Line{b[x],b[x]*dis(x,t)+a[x]+F[x]});
}
vector<long long> travel(vector<long long> A,vector<int> B,vector<int> U,vector<int> V,vector<int> W){
    n=A.size();
	for(int i=1;i<=n;++i) a[i]=A[i-1],b[i]=B[i-1];
	for(int i=0;i<n-1;++i){
		++U[i],++V[i],
		G[U[i]].push_back({V[i],W[i]}),
		G[V[i]].push_back({U[i],W[i]});
	}
	dfs(1,0),ctp(1,1);
	ASD::work();
	for(int i=1;i<=n;++i) st[i]=i;
	sort(st+1,st+n+1,[](int x,int y){return b[x]<b[y];}),tp=n;
	while(st[tp]!=1) --tp;
	while(tp){
		int x=st[tp--];
		if(x!=1) F[x]=0x7fffffffffffffff,cal(x);
		ins(x);
	}
	for(int i=2;i<=n;++i) cal(i);
	return vector<long long>(F+2,F+n+1);
}