#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>

#define fi first
#define se second
#define mkp std::make_pair
using ll=long long;
using std::max;
using std::min;
template<class T> void cmax(T&a,T b){a=max(a,b);}
template<class T> void cmin(T&a,T b){a=min(a,b);}

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();
    std::vector<std::vector<std::pair<int,int> > > G(N);
    std::vector<ll> vdep(N);
    std::vector<std::vector<int> > fp(17,std::vector<int>(N));
    std::vector<int> dfn(N);
    int dfc=0;
    auto dmin=[&](int x,int y){return dfn[x]<dfn[y]?x:y;};
    auto dfslca=[&](auto&&self,int x,int p)->void{
        fp[0][dfn[x]=dfc++]=p;
        for(auto t:G[x]) if(t.fi!=p){
            vdep[t.fi]=vdep[x]+t.se;
            self(self,t.fi,x);
        }
    };
    auto getlca=[&](int x,int y){
        if(x==y) return x;
        if((x=dfn[x])>(y=dfn[y])) std::swap(x,y);
        int lg=std::__lg(y-x++);
        return dmin(fp[lg][x],fp[lg][y-(1<<lg)+1]);
    };
    auto getdis=[&](int x,int y){
        return vdep[x]+vdep[y]-2*vdep[getlca(x,y)];
    };
    for(int i=0;i<N-1;++i){
        G[U[i]].emplace_back(V[i],W[i]);
        G[V[i]].emplace_back(U[i],W[i]);
    }
    dfslca(dfslca,0,0);
    for(int j=1;j<17;++j) for(int i=0;i+(1<<j)-1<N;++i){
        fp[j][i]=dmin(fp[j-1][i],fp[j-1][i+(1<<j-1)]);
    }
    const ll INF=0x3f3f3f3f3f3f3f3f;
    std::vector<ll> f(N,INF);
    std::vector<int> p(N);
    for(int i=0;i<N;++i) p[i]=i;
    std::sort(p.begin(),p.end(),[&](int x,int y){
            return B[x]>B[y];});
    f[0]=0;
    std::vector<ll> dis(N);
    using P=std::pair<ll,std::pair<int,int> >;
    std::priority_queue<P,std::vector<P>,std::greater<P> > q;
    for(int wtf=0;wtf<2;++wtf)
    for(int i=0;i<N;){
        int j=i;
        for(;j<N&&B[p[i]]==B[p[j]];++j);
        std::fill(dis.begin(),dis.end(),INF);
        for(int k=i;k<j;++k){
            q.emplace(dis[p[k]]=A[p[k]]+f[p[k]],mkp(p[k],p[k]));
        }
        while(q.size()){
            auto p=q.top();
            q.pop();
            int x=p.se.fi;
            if(dis[x]<p.fi) continue;
            for(auto e:G[x]) if(dis[e.fi]>dis[x]+e.se*B[p.se.se]){
                q.emplace(dis[e.fi]=dis[x]+e.se*B[p.se.se],mkp(e.fi,p.se.se));
                cmin(f[e.fi],dis[e.fi]);
            }
        }
        i=j;
    }
    return std::vector<ll>(f.begin()+1,f.end());
}