#include<bits/stdc++.h>
#define poly vector<int>
#define IOS ios::sync_with_stdio(false)
#define ll long long
#define mp make_pair
#define mt make_tuple
#define pa pair < int,int >
#define fi first
#define se second
#define mod 998244353
#define sz(x) (int)((x).size())
// #define int ll
//#define N
using namespace std;
const int N=500005,inf=1e9+1;
int siz[N],Son[N],dep[N];
int lson[N],rson[N],rfa[N],All[N],Tp[N],pos[N];
int tim[N],TIM;
int mn[N],tot[N],smn[N],tag[N],a[N];
ll sm[N];
int n,son[N][2];
int Lim[N],val[N];
int siz1[N],son1[N];
poly G[N];
ll ans[N];
int ffa[N];
int fail[N];
bool vis[N];
inline int build(poly &g,poly &g1,int l,int r,int Dep=0)
{
    if (l>r) return 0;
    int mid=lower_bound(g1.begin()+l,g1.begin()+r+1,(g1[l]+g1[r])/2)-g1.begin();
    int u=g[mid];
    lson[u]=build(g,g1,l,mid-1,Dep+1);
    rson[u]=build(g,g1,mid+1,r,Dep+1);
    All[u]=All[lson[u]]+All[rson[u]]+1;
    return u;
}
inline void chk(int k)
{
    if (k==0) return;
    if (tim[k]!=TIM) 
        tag[k]=mn[k]=sm[k]=a[k]=0,smn[k]=inf,tot[k]=All[k],tim[k]=TIM;
}
inline void ptag(int k,int x)
{
    if (k==0) return;
    if (a[k]==mn[k]) a[k]+=x;
    mn[k]+=x;
    sm[k]+=1ll*x*tot[k];
    tag[k]+=x;
}
inline void pushdown(int k)
{
    chk(lson[k]);chk(rson[k]);
    if (!tag[k]) return;
    if (mn[lson[k]]+tag[k]==mn[k])
        ptag(lson[k],tag[k]);
    if (mn[rson[k]]+tag[k]==mn[k])
        ptag(rson[k],tag[k]);
    tag[k]=0;
}
inline void pushup(int k)
{
    sm[k]=a[k]+sm[lson[k]]+sm[rson[k]];
    mn[k]=mn[lson[k]],tot[k]=tot[lson[k]],smn[k]=smn[lson[k]];
    if (a[k]<mn[k]) smn[k]=mn[k],tot[k]=1,mn[k]=a[k];
    else
    if (a[k]==mn[k]) tot[k]++;
    else
    if (a[k]<smn[k]) smn[k]=a[k];
    if (mn[rson[k]]<mn[k])
    {
        smn[k]=mn[k],mn[k]=mn[rson[k]],tot[k]=tot[rson[k]];
    } else
    if (mn[rson[k]]==mn[k])
    {
        tot[k]+=tot[rson[k]];
    } else
    if (mn[rson[k]]<smn[k])
    {
        smn[k]=mn[rson[k]];
    }
    if (smn[rson[k]]<smn[k]) smn[k]=smn[rson[k]];
}
inline void upd1(int k,int y)
{
    if (!k) return;
    chk(k); 
    pushdown(k);
    if (y>=smn[k])
    {
        a[k]=max(a[k],y);
        upd1(lson[k],y);
        upd1(rson[k],y);
        pushup(k);
    } else
    if (y<smn[k]&&y>mn[k])
    {
        ptag(k,y-mn[k]);
    }
}
inline void upd(int k,int l,int r,int y)
{
    if (!k) return;
    if (r-l+1==All[k])
    {
        upd1(k,y);
        return;
    }
    chk(k);
    pushdown(k);
    if (l<=pos[k]&&pos[k]<=r) a[k]=max(a[k],y);
    if (l<pos[k]) upd(lson[k],l,min(r,pos[k]-1),y);
    if (r>pos[k]) upd(rson[k],max(l,pos[k]+1),r,y);
    pushup(k);
}
inline ll qry(int k,int l,int r)
{
    if (!k) return 0;
    chk(k);
    if (r-l+1==All[k]) return sm[k];
    pushdown(k);
    ll res=0;
    if (l<=pos[k]&&pos[k]<=r) res+=a[k];
    if (l<pos[k]) res+=qry(lson[k],l,min(r,pos[k]-1));
    if (r>pos[k]) res+=qry(rson[k],max(l,pos[k]+1),r);
    return res;
}
void dfs(int k)
{
    siz1[k]=1;son1[k]=0;
    for (auto u:G[k])
    {
        dfs(u);
        siz1[k]+=siz1[u];
        if (siz1[u]>siz1[son1[k]]) son1[k]=u;
    }
}
inline void ins(int k)
{
    int v=val[k];
    int L=Lim[k];
    while (k)
    {
        if (pos[k]-dep[k]+L>=0) 
        {
            upd(Tp[k],pos[k]-dep[k]+L,pos[k],v);
            break;
        }
        upd(Tp[k],0,pos[k],v);
        k=rfa[Tp[k]];
    }
}
inline ll qry(int k)
{
    ll res=0;
    while (k)
    {
        res+=qry(Tp[k],0,pos[k]);
        k=rfa[Tp[k]];
    }
    return res;
}
void ins(int k,int fa)
{
    ins(k);
    for (auto u:G[k])
    {
        ins(u,k);
    }
}
void dfs1(int k)
{
    for (auto u:G[k])
    {
        if (u==son1[k]) continue;
        dfs1(u);
        TIM++;
    }
    if (son1[k]) dfs1(son1[k]);
    ins(k);
    for (auto u:G[k])
    {
        if (u==son1[k]) continue;
        ins(u,k);
    }
    ans[k]=qry(k);
}  
void BellaKira()
{
    mn[0]=inf,smn[0]=inf;
    ++TIM;
    cin>>n;
    for (int i=1;i<=n;i++) 
    {
        ans[i]=All[i]=son[i][0]=son[i][1]=0,vis[i]=0,poly().swap(G[i]);
        siz[i]=0,Son[i]=dep[i]=lson[i]=rson[i]=rfa[i]=All[i]=Tp[i]=pos[i]=0;   
    }
// int siz[N],Son[N],dep[N];
// int lson[N],rson[N],rfa[N],All[N],Tp[N],pos[N];
// int tim[N],TIM;
// int mn[N],tot[N],smn[N],tag[N],a[N];
// ll sm[N];
// int n,son[N][2];
// int Lim[N],val[N];
// int siz1[N],son1[N];
// poly G[N];
// ll ans[N];
// int ffa[N];
// int fail[N];
// bool vis[N];
    for (int i=1;i<=n;i++) chk(i);
    ++TIM;
    for (int i=2;i<=n;i++)
    {
        int x,y;
        cin>>x>>y;
        son[x][y]=i;
        ffa[i]=x;
        dep[i]=dep[x]+1;
    }
    for (int i=1;i<=n;i++) cin>>val[i];
    for (int i=1;i<=n;i++) cin>>Lim[i];
    for (int i=n;i>=1;i--)
    {
        siz[i]=1;Son[i]=0;
        for (int w=0;w<2;w++)
        {
            int u=son[i][w];
            if (!u) continue;
            siz[i]+=siz[u];
            if (siz[u]>siz[Son[i]]) Son[i]=u;
        }
    }
    for (int i=n;i>=1;i--)
        if (!vis[i])
        {
            int x=i;
            poly g,gg;
            while (1)
            {
                g.push_back(x);vis[x]=1;
                if (Son[ffa[x]]!=x) break;
                x=ffa[x];
            }
            reverse(g.begin(),g.end());
            gg=g;
            for (int i=0;i<sz(g);i++) pos[g[i]]=i;
            for (auto &u:gg)
                u=siz[u]-siz[Son[u]];
            for (int j=1;j<sz(gg);j++) gg[j]+=gg[j-1];
            int rt=build(g,gg,0,sz(g)-1);
            rfa[rt]=ffa[x];
            for (auto u:g)
                Tp[u]=rt;
        }
    queue<int>q;
    q.push(1);
    fail[1]=0;
    for (int i=0;i<2;i++) son[0][i]=1;
    while (!q.empty())
    {
        int u=q.front();q.pop();
        for (int i=0;i<2;i++)
        {
            if (son[u][i])
            {
                fail[son[u][i]]=son[fail[u]][i];
                q.push(son[u][i]);
            } else son[u][i]=son[fail[u]][i];
        }
    }
    for (int i=2;i<=n;i++)
        G[fail[i]].push_back(i);
    dfs(1);
    dfs1(1);
    for (int i=1;i<=n;i++) cout<<ans[i]<<" ";
    cout<<'\n';
}
signed main()
{
    IOS;
    cin.tie(0);
    int T=1;
    cin>>T;
    while (T--)
    {
        BellaKira();
    }
}