Problem: Polycarp is an organizer of a Berland ICPC regional event. There are n universities in Berland numbered from 1 to n. Polycarp knows all competitive programmers in the region. There are n students: the i-th student is enrolled at a university u_i and has a programming skill s_i.

Polycarp has to decide on the rules now. In particular, the number of members in the team.

Polycarp knows that if he chooses the size of the team to be some integer k, each university will send their k strongest (with the highest programming skill s) students in the first team, the next k strongest students in the second team and so on. If there are fewer than k students left, then the team can't be formed. Note that there might be universities that send zero teams.

The strength of the region is the total skill of the members of all present teams. If there are no teams present, then the strength is 0.

Help Polycarp to find the strength of the region for each choice of k from 1 to n.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

The first line of each testcase contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of universities and the number of students.

The second line of each testcase contains n integers u_1, u_2, ..., u_n (1 ≤ u_i ≤ n) — the university the i-th student is enrolled at.

The third line of each testcase contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 10^9) — the programming skill of the i-th student.

The sum of n over all testcases doesn't exceed 2 ⋅ 10^5.

Output

For each testcase print n integers: the strength of the region — the total skill of the members of the present teams — for each choice of team size k.

Example

Input


4
7
1 2 1 2 1 2 1
6 8 3 1 5 1 5
10
1 1 1 2 2 2 2 3 3 3
3435 3014 2241 2233 2893 2102 2286 2175 1961 2567
6
3 3 3 3 3 3
5 9 6 7 9 7
1
1
3083


Output


29 28 26 19 0 0 0 
24907 20705 22805 9514 0 0 0 0 0 0 
43 43 43 32 38 43 
3083 

Note

In the first testcase the teams from each university for each k are: 

  * k=1: 
    * university 1: [6], [5], [5], [3]; 
    * university 2: [8], [1], [1]; 
  * k=2: 
    * university 1: [6, 5], [5, 3]; 
    * university 2: [8, 1]; 
  * k=3: 
    * university 1: [6, 5, 5]; 
    * university 2: [8, 1, 1]; 
  * k=4: 
    * university 1: [6, 5, 5, 3]; 

Solution (in CPP):

Solution:
#include<bits/stdc++.h>				//Written by ThiDaiLoc
using namespace std;
typedef long long ll;				
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll,ll> pll;
typedef pair<ll,pll> trp;
typedef vector<ll> vi;
typedef vector<pll> vp;

#define fu(i,a,b)   for(ll i=a;i<=b;i++)
#define f1(i,n)     for(ll i=1;i<=n;i++)
#define fs(i,s)     for(ll i=0;i+1<=s.length();i++)
#define fd(i,b,a)   for(ll i=b;i>=a;i--)
#define fuv(i,a)    for(ll i=0;i<a.size();i++)
#define fdv(i,a)    for(ll i=(ll)a.size()-1;i>=0;i--)
#define ms(a,x)     memset(a, x, sizeof a)
#define prec(n)     fixed<<setprecision(n)
#define uni(a)      (a).erase(unique(all(a)), (a).end())
#define pb(i)       push_back(i)
#define pob         pop_back()
#define sc(a)       cin>>a
#define sc2(a,b)    cin>>a>>b
#define sc3(a,b,c)  cin>>a>>b>>c
#define pr(a)       cout<<a<<endl
#define pr2(a,b)    cout<<a<<" "<<b<<endl
#define rpr(a)      return cout<<a<<endl,0
#define prY         cout<<"YES"<<endl
#define prN         cout<<"NO"<<endl
#define bit(n,i)    (((n)>>(i))&1)
#define lowb(a,n,x) lower_bound(a,a+n,x) -a
#define lowb2(a,x)  lower_bound(all(a),x) -a.begin()
#define all(x)      (x).begin(), (x).end()
#define sz(a)       (ll)a.size()
#define le(s)       (ll)s.length()		
#define re          return 	
#define	mp(a,b)     make_pair(a,b)
#define	mp3(a,b,c)  make_pair(a,make_pair(b,c))
#define se          second
#define fi          first 
#define sse         second.second
#define sfi         second.first
#define soA         sort(A+1,A+1+n)
#define so(A,n)     sort(A+1,A+1+n)
#define sov(v)      sort(all(v))
#define sovr(v)     sort(all(v),greater<ll>())
#define debug(x)    cerr << #x << " = " << x << endl
#define INPUT       freopen("locin.txt", "r", stdin)
#define OUTPUT      freopen("locout.txt", "w", stdout)
inline ll isqrt(ll k) {ll r = sqrt(k) + 1; while (r * r > k) r--; return r;}
inline ll icbrt(ll k) {ll r = cbrt(k) + 1; while (r * r * r > k) r--; return r;}
inline ll mnz(ll& a,ll b){return a=(a>b?b:a);}
inline ll mxz(ll& a,ll b){return a=(a<b?b:a);}
inline string toString(ll n) {stringstream ss; ss << n;return ss.str();}
double const eps = 1e-6;
ll const Base=1e9+7,oo=1e17,MAXN=1e6;


ll A[MAXN+5],B[MAXN+5],Aans[MAXN+5];
vi dske[MAXN+5];
ll Solves(){
	
	ll n,m,k,cnt=0,ans=0,x,y,q,c,sum=0,v,t;
	// PROCESS IN HERE
	sc(n);
	f1(i,n)dske[i].clear(),dske[i].pb(0),Aans[i]=0;
	f1(i,n){
		sc(A[i]);
	}
	f1(i,n){
		sc(B[i]);
		dske[A[i]].pb(B[i]);
	}
	
	f1(i,n){
		sort(dske[i].begin()+1,dske[i].end());
		reverse(dske[i].begin()+1,dske[i].end());
		fu(j,1,sz(dske[i])-1){
			dske[i][j]+=dske[i][j-1];
		}
	}
	f1(i,n){
		c=sz(dske[i])-1;
		fu(j,1,c){
			t=c/j*j;
			Aans[j]+=dske[i][t];
		}
	}
	
	f1(i,n){
		cout<<Aans[i]<<" ";
	
	}
		pr("");
	
	re 0;
	// Hack it if you can :)
}

int main(){
	//INPUT;
	if(fopen("locin.txt", "r"))INPUT;
	ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	ll test=1;
	sc(test);
	fu(T,1,test){
//		cout<<"Case #"<<T<<": ";
		Solves();
	} 		
}